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Trigonometry (sine & cosine rules)
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49 questions at your level
Difficulty
All
Level 3
Level 4
Level 5
The sine rule
16 questions
Lesson
Not started
Mark as done
In triangle
A
B
C
ABC
A
B
C
, angle
A
=
52
°
A = 52°
A
=
52°
, angle
B
=
71
°
B = 71°
B
=
71°
and
a
=
8.4
a = 8.4
a
=
8.4
cm.
8.4 cm
b
52°
71°
A
B
C
Diagram NOT accurately drawn
Work out the length of
b
b
b
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
In triangle
P
Q
R
PQR
P
QR
,
p
=
12.6
p = 12.6
p
=
12.6
cm,
q
=
9.4
q = 9.4
q
=
9.4
cm and angle
P
=
48
°
P = 48°
P
=
48°
.
Angle
Q
Q
Q
is acute.
Work out the size of angle
Q
Q
Q
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
, angle
A
=
61
°
A = 61°
A
=
61°
, angle
C
=
47
°
C = 47°
C
=
47°
and
c
=
10.5
c = 10.5
c
=
10.5
cm.
Work out the length of
a
a
a
. Give your answer correct to 3 significant figures.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
In triangle
P
Q
R
PQR
P
QR
,
p
=
7.8
p = 7.8
p
=
7.8
cm, angle
P
=
42
°
P = 42°
P
=
42°
and angle
R
=
66
°
R = 66°
R
=
66°
.
Work out the length of
r
r
r
. Give your answer correct to 3 significant figures.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
8.6 cm
38°
65°
P
Q
R
Diagram NOT accurately drawn
In triangle
P
Q
R
PQR
P
QR
,
P
Q
=
8.6
PQ = 8.6
P
Q
=
8.6
cm, angle
Q
P
R
=
38
°
QPR = 38°
QP
R
=
38°
and angle
P
Q
R
=
65
°
PQR = 65°
P
QR
=
65°
.
Work out the length of
Q
R
QR
QR
.
Give your answer correct to 3 significant figures. (4 marks)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
a
=
8.4
a = 8.4
a
=
8.4
cm, angle
A
=
42
°
A = 42°
A
=
42°
and angle
B
=
65
°
B = 65°
B
=
65°
.
(a)
Work out the length of
b
b
b
. Give your answer correct to 3 significant figures. [3]
(b)
Work out the length of
c
c
c
. Give your answer correct to 3 significant figures. [2]
●●●
●●
Level 3
5 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
, angle
A
=
43
°
A = 43°
A
=
43°
, angle
B
=
68
°
B = 68°
B
=
68°
and
c
=
15.2
c = 15.2
c
=
15.2
cm.
(a)
Work out the size of angle
C
C
C
.
(b)
Work out the length of
a
a
a
. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A surveyor stands at point
A
A
A
and sights a mast at point
C
C
C
. She then walks to point
B
B
B
.
In triangle
A
B
C
ABC
A
B
C
, angle
A
=
35
°
A = 35°
A
=
35°
, angle
C
=
104
°
C = 104°
C
=
104°
and
b
=
27
b = 27
b
=
27
m.
(a)
Work out the size of angle
B
B
B
.
(b)
Work out the distance
a
a
a
. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
In triangle
X
Y
Z
XYZ
X
Y
Z
,
x
=
11.2
x = 11.2
x
=
11.2
cm,
y
=
8.6
y = 8.6
y
=
8.6
cm and angle
X
=
74
°
X = 74°
X
=
74°
.
Angle
Y
Y
Y
is acute.
Work out the size of angle
Y
Y
Y
. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
b
=
14
b = 14
b
=
14
cm, angle
A
=
30
°
A = 30°
A
=
30°
and angle
B
=
110
°
B = 110°
B
=
110°
.
(a)
Work out the length of
a
a
a
. Give your answer correct to 3 significant figures.
(b)
Work out the length of
c
c
c
. Give your answer correct to 3 significant figures.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
B
C
=
9.5
BC = 9.5
B
C
=
9.5
cm,
A
C
=
7
AC = 7
A
C
=
7
cm and angle
B
A
C
=
68
°
BAC = 68°
B
A
C
=
68°
.
Angle
A
B
C
ABC
A
B
C
is acute.
(a)
Work out the size of angle
A
B
C
ABC
A
B
C
. Give your answer correct to 1 decimal place. (3 marks)
(b)
Work out the area of triangle
A
B
C
ABC
A
B
C
. Give your answer correct to 3 significant figures. (2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
In triangle
P
Q
R
PQR
P
QR
,
P
Q
=
10.4
PQ = 10.4
P
Q
=
10.4
cm,
Q
R
=
8.7
QR = 8.7
QR
=
8.7
cm and angle
P
Q
R
=
58
°
PQR = 58°
P
QR
=
58°
.
10.4 cm
8.7 cm
58°
P
Q
R
Diagram NOT accurately drawn
(a)
Work out the length of
P
R
PR
P
R
. Give your answer correct to 3 significant figures. [3]
(b)
Work out the size of angle
Q
P
R
QPR
QP
R
. Give your answer correct to 1 decimal place. [2]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
b
=
9.1
b = 9.1
b
=
9.1
cm,
c
=
12.4
c = 12.4
c
=
12.4
cm and angle
B
=
39
°
B = 39°
B
=
39°
.
Angle
C
C
C
is
obtuse
.
Work out the size of angle
C
C
C
. Give your answer correct to 1 decimal place.
●●●●●
Level 5
4 marks
Start
→
Mark as done
Two people,
A
A
A
and
B
B
B
, stand on level ground on the same side of a vertical tower, in line with its base.
A
A
A
and
B
B
B
are
50
50
50
m apart, and
B
B
B
is nearer the tower.
From
A
A
A
the angle of elevation of the top of the tower,
T
T
T
, is
32
°
32°
32°
. From
B
B
B
the angle of elevation of
T
T
T
is
55
°
55°
55°
.
(a)
Work out the length
B
T
BT
B
T
. Give your answer correct to 3 significant figures.
(b)
Hence work out the height of the tower. Give your answer correct to 3 significant figures.
●●●●●
Level 5
4 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a quadrilateral.
9.4 cm
112°
41°
63°
A
B
C
D
A
B
=
9.4
AB = 9.4
A
B
=
9.4
cm \qquad angle
A
B
C
=
112
°
ABC = 112°
A
B
C
=
112°
\qquad angle
C
A
D
=
41
°
CAD = 41°
C
A
D
=
41°
\qquad angle
A
C
D
=
63
°
ACD = 63°
A
C
D
=
63°
The area of triangle
A
B
C
ABC
A
B
C
is
38
38
38
cm²
Calculate the area of triangle
A
C
D
ACD
A
C
D
.
Give your answer correct to 3 significant figures.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a quadrilateral.
8 cm
9.5 cm
11 cm
72°
58°
A
B
C
D
A
B
=
8
AB = 8
A
B
=
8
cm \qquad
A
D
=
11
AD = 11
A
D
=
11
cm \qquad
C
D
=
9.5
CD = 9.5
C
D
=
9.5
cm
angle
B
A
D
=
72
°
BAD = 72°
B
A
D
=
72°
\qquad angle
B
C
D
=
58
°
BCD = 58°
B
C
D
=
58°
Find the size of angle
B
D
C
BDC
B
D
C
.
Give your answer correct to the nearest degree.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
The cosine rule
22 questions
Lesson
Not started
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
b
=
9
b = 9
b
=
9
cm,
c
=
13
c = 13
c
=
13
cm and angle
A
=
67
°
A = 67°
A
=
67°
.
13 cm
a
9 cm
67°
A
B
C
Diagram NOT accurately drawn
Work out the length of
a
a
a
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
b
=
8.2
b = 8.2
b
=
8.2
cm,
c
=
6.5
c = 6.5
c
=
6.5
cm and angle
A
=
54
°
A = 54°
A
=
54°
.
Work out the length of
a
a
a
. Give your answer correct to 3 significant figures.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A triangular field has two sides of length
8
8
8
m and
15
15
15
m, with an angle of
70
°
70°
70°
between them.
(a)
Work out the area of the field. Give your answer correct to 1 decimal place.
(b)
Work out the length of the third side. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
A triangle has sides of length
6
6
6
cm,
9
9
9
cm and
11
11
11
cm.
Work out the size of the largest angle of the triangle. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A triangle has sides of length
7
7
7
cm,
8
8
8
cm and
12
12
12
cm.
Work out the size of the smallest angle of the triangle. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A ship sails
40
40
40
km from port
A
A
A
to a buoy
B
B
B
. It then turns and sails
65
65
65
km from
B
B
B
to port
C
C
C
.
Angle
A
B
C
=
105
°
ABC = 105°
A
B
C
=
105°
.
Work out the direct distance from
A
A
A
to
C
C
C
. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A triangle has sides of length
5
5
5
cm,
7
7
7
cm and
10
10
10
cm.
Work out the size of the largest angle of the triangle. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
a
=
11.4
a = 11.4
a
=
11.4
cm,
b
=
9.7
b = 9.7
b
=
9.7
cm and
c
=
6.8
c = 6.8
c
=
6.8
cm.
Work out the size of angle
A
A
A
. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A parallelogram has sides of length
6
6
6
cm and
9
9
9
cm, and one of its angles is
120
°
120°
120°
.
Work out the length of the longer diagonal. Give your answer correct to 3 significant figures.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
A
B
=
8
AB = 8
A
B
=
8
cm,
A
C
=
11
AC = 11
A
C
=
11
cm and angle
B
A
C
=
52
°
BAC = 52°
B
A
C
=
52°
.
(a)
Work out the length of
B
C
BC
B
C
. Give your answer correct to 3 significant figures. (3 marks)
(b)
Work out the area of triangle
A
B
C
ABC
A
B
C
. Give your answer correct to 3 significant figures. (2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
A triangle has sides of length
7
7
7
cm,
9
9
9
cm and
12
12
12
cm.
Work out the size of the largest angle. Give your answer correct to 1 decimal place. (3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
9.2 cm
7.5 cm
64°
A
B
C
Diagram NOT accurately drawn
In triangle
A
B
C
ABC
A
B
C
,
A
B
=
9.2
AB = 9.2
A
B
=
9.2
cm,
A
C
=
7.5
AC = 7.5
A
C
=
7.5
cm and angle
B
A
C
=
64
°
BAC = 64°
B
A
C
=
64°
.
(a)
Work out the length of
B
C
BC
B
C
. Give your answer correct to 3 significant figures. (3 marks)
(b)
Work out the area of triangle
A
B
C
ABC
A
B
C
. Give your answer correct to 3 significant figures. (2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
In triangle
P
Q
R
PQR
P
QR
,
P
Q
=
10.4
PQ = 10.4
P
Q
=
10.4
cm,
Q
R
=
8.7
QR = 8.7
QR
=
8.7
cm and angle
P
Q
R
=
58
°
PQR = 58°
P
QR
=
58°
.
10.4 cm
8.7 cm
58°
P
Q
R
Diagram NOT accurately drawn
(a)
Work out the length of
P
R
PR
P
R
. Give your answer correct to 3 significant figures. [3]
(b)
Work out the size of angle
Q
P
R
QPR
QP
R
. Give your answer correct to 1 decimal place. [2]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
A
B
=
5
AB = 5
A
B
=
5
cm,
A
C
=
7
AC = 7
A
C
=
7
cm and angle
B
A
C
=
60
°
BAC = 60°
B
A
C
=
60°
.
(a)
Work out the exact length of
B
C
BC
B
C
. [3]
(b)
Work out the exact area of the triangle. [2]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
A triangle has sides of length
6
6
6
cm,
8
8
8
cm and
11
11
11
cm.
(a)
Work out the size of the largest angle. Give your answer correct to 1 decimal place. [3]
(b)
Work out the area of the triangle. Give your answer correct to 3 significant figures. [2]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
O
P
Q
OPQ
O
P
Q
is a triangle.
O
Q
R
OQR
O
QR
is a sector of a circle, centre
O
O
O
.
O
Q
R
58°
7.4 cm
5.8 cm
118°
P
Calculate the area of the sector
O
Q
R
OQR
O
QR
.
Give your answer correct to 3 significant figures.
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A ship leaves a harbour
H
H
H
and sails
11
11
11
km on a bearing of
062
°
062°
062°
to a point
A
A
A
.
It then sails
8
8
8
km on a bearing of
145
°
145°
145°
to a point
B
B
B
.
11 km
8 km
H
A
B
N
N
Diagram NOT accurately drawn
(a)
Show that angle
H
A
B
=
97
°
HAB = 97°
H
A
B
=
97°
.
(b)
Work out the distance
H
B
HB
H
B
. Give your answer correct to 1 decimal place.
(c)
Work out the bearing of
B
B
B
from
H
H
H
. Give your answer correct to the nearest degree.
●●●●●
Level 5
8 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
b
=
7.5
b = 7.5
b
=
7.5
cm,
c
=
10.2
c = 10.2
c
=
10.2
cm and angle
A
=
118
°
A = 118°
A
=
118°
.
10.2 cm
a
7.5 cm
118°
Diagram NOT accurately drawn
(a)
Work out the length of
a
a
a
. Give your answer correct to 1 decimal place.
(b)
Explain why
a
a
a
must be longer than
7.5
2
+
10.2
2
\sqrt{7.5^2 + 10.2^2}
7.
5
2
+
10.
2
2
.
●●●●●
Level 5
5 marks
Start
→
Mark as done
Two ships leave a port at the same time. Ship
A
A
A
sails
12
12
12
km on a bearing of
040
°
040°
040°
. Ship
B
B
B
sails
18
18
18
km on a bearing of
115
°
115°
115°
.
Work out the distance between the two ships. Give your answer correct to 3 significant figures.
●●●●●
Level 5
4 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a quadrilateral.
9.4 cm
112°
41°
63°
A
B
C
D
A
B
=
9.4
AB = 9.4
A
B
=
9.4
cm \qquad angle
A
B
C
=
112
°
ABC = 112°
A
B
C
=
112°
\qquad angle
C
A
D
=
41
°
CAD = 41°
C
A
D
=
41°
\qquad angle
A
C
D
=
63
°
ACD = 63°
A
C
D
=
63°
The area of triangle
A
B
C
ABC
A
B
C
is
38
38
38
cm²
Calculate the area of triangle
A
C
D
ACD
A
C
D
.
Give your answer correct to 3 significant figures.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a quadrilateral.
8 cm
9.5 cm
11 cm
72°
58°
A
B
C
D
A
B
=
8
AB = 8
A
B
=
8
cm \qquad
A
D
=
11
AD = 11
A
D
=
11
cm \qquad
C
D
=
9.5
CD = 9.5
C
D
=
9.5
cm
angle
B
A
D
=
72
°
BAD = 72°
B
A
D
=
72°
\qquad angle
B
C
D
=
58
°
BCD = 58°
B
C
D
=
58°
Find the size of angle
B
D
C
BDC
B
D
C
.
Give your answer correct to the nearest degree.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
The diagram shows a circle, centre
O
O
O
, radius
r
r
r
cm, and two regular octagons.
r cm
O
The sides of the larger octagon are tangents to the circle.
The vertices of the smaller octagon lie on the circle.
By considering perimeters, show that
4
2
−
2
<
π
<
8
(
2
−
1
)
4\sqrt{2 - \sqrt{2}} < \pi < 8(\sqrt{2} - 1)
4
2
−
2
<
π
<
8
(
2
−
1
)
(4 marks)
●●●●●
Level 5
4 marks
Start
→
Area of a triangle & 3D trigonometry
21 questions
Lesson
Not started
Mark as done
The diagram shows a triangle with two sides of length
9.4
9.4
9.4
cm and
12.7
12.7
12.7
cm, and an angle of
58
°
58°
58°
between them.
12.7 cm
9.4 cm
58°
Diagram NOT accurately drawn
Work out the area of the triangle. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
A triangle has two sides of length
7.5
7.5
7.5
cm and
9.2
9.2
9.2
cm, and the angle between them is
41
°
41°
41°
.
Work out the area of the triangle. Give your answer correct to 3 significant figures.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
A triangle has two sides of length
11
11
11
cm and
14
14
14
cm, and an area of
42
42
42
cm².
The angle between the two given sides is acute.
Work out the size of this angle. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A triangular field has two sides of length
8
8
8
m and
15
15
15
m, with an angle of
70
°
70°
70°
between them.
(a)
Work out the area of the field. Give your answer correct to 1 decimal place.
(b)
Work out the length of the third side. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
A triangle has two sides of length
8
8
8
cm and
10
10
10
cm, and an area of
30
30
30
cm
2
^2
2
.
The angle between the two given sides is acute.
Work out the size of this angle. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A cuboid measures
8
8
8
cm by
6
6
6
cm by
5
5
5
cm.
Work out the length of the longest diagonal of the cuboid. Give your answer correct to 3 significant figures.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A cuboid measures
8
8
8
cm by
6
6
6
cm by
5
5
5
cm.
Work out the angle between the longest diagonal of the cuboid and the base. Give your answer correct to 1 decimal place.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
A
B
=
8
AB = 8
A
B
=
8
cm,
A
C
=
11
AC = 11
A
C
=
11
cm and angle
B
A
C
=
52
°
BAC = 52°
B
A
C
=
52°
.
(a)
Work out the length of
B
C
BC
B
C
. Give your answer correct to 3 significant figures. (3 marks)
(b)
Work out the area of triangle
A
B
C
ABC
A
B
C
. Give your answer correct to 3 significant figures. (2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
B
C
=
9.5
BC = 9.5
B
C
=
9.5
cm,
A
C
=
7
AC = 7
A
C
=
7
cm and angle
B
A
C
=
68
°
BAC = 68°
B
A
C
=
68°
.
Angle
A
B
C
ABC
A
B
C
is acute.
(a)
Work out the size of angle
A
B
C
ABC
A
B
C
. Give your answer correct to 1 decimal place. (3 marks)
(b)
Work out the area of triangle
A
B
C
ABC
A
B
C
. Give your answer correct to 3 significant figures. (2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
9.2 cm
7.5 cm
64°
A
B
C
Diagram NOT accurately drawn
In triangle
A
B
C
ABC
A
B
C
,
A
B
=
9.2
AB = 9.2
A
B
=
9.2
cm,
A
C
=
7.5
AC = 7.5
A
C
=
7.5
cm and angle
B
A
C
=
64
°
BAC = 64°
B
A
C
=
64°
.
(a)
Work out the length of
B
C
BC
B
C
. Give your answer correct to 3 significant figures. (3 marks)
(b)
Work out the area of triangle
A
B
C
ABC
A
B
C
. Give your answer correct to 3 significant figures. (2 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
In triangle
A
B
C
ABC
A
B
C
,
A
B
=
5
AB = 5
A
B
=
5
cm,
A
C
=
7
AC = 7
A
C
=
7
cm and angle
B
A
C
=
60
°
BAC = 60°
B
A
C
=
60°
.
(a)
Work out the exact length of
B
C
BC
B
C
. [3]
(b)
Work out the exact area of the triangle. [2]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
A cuboid measures
12
12
12
cm by
5
5
5
cm by
8
8
8
cm.
(a)
Work out the length of the longest diagonal of the cuboid. Give your answer correct to 3 significant figures. [2]
(b)
Work out the angle between this diagonal and the
12
12
12
cm by
5
5
5
cm base. Give your answer correct to 1 decimal place. [3]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
A triangle has sides of length
6
6
6
cm,
8
8
8
cm and
11
11
11
cm.
(a)
Work out the size of the largest angle. Give your answer correct to 1 decimal place. [3]
(b)
Work out the area of the triangle. Give your answer correct to 3 significant figures. [2]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The diagram shows a circle of radius
10
10
10
cm. A chord divides the circle, and the angle at the centre is
80
°
80°
80°
.
O
10 cm
80°
Diagram NOT accurately drawn
Work out the area of the shaded segment. Give your answer correct to 1 decimal place.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The diagram shows a cuboid measuring
12
12
12
cm by
5
5
5
cm by
9
9
9
cm.
12 cm
9 cm
5 cm
Diagram NOT accurately drawn
Work out the angle between the long diagonal of the cuboid and its base. Give your answer correct to 1 decimal place.
●●●●●
Level 5
3 marks
Start
→
Mark as done
The diagram shows a pyramid with a square base of side
10
10
10
cm. Each sloping edge has length
13
13
13
cm.
10 cm
13 cm
Diagram NOT accurately drawn
(a)
Work out the vertical height of the pyramid. Give your answer correct to 1 decimal place.
(b)
Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.
●●●●●
Level 5
5 marks
Start
→
Mark as done
A pyramid has a square base of side
12
12
12
cm and a vertical height of
8
8
8
cm. The apex is directly above the centre of the base.
Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.
●●●●●
Level 5
3 marks
Start
→
Mark as done
A pyramid has a square base of side
8
8
8
cm. The apex
V
V
V
is directly above the centre of the base, at a height of
6
6
6
cm.
(a)
Work out the length of a sloping edge of the pyramid. Give your answer correct to 3 significant figures. [3]
(b)
Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place. [2]
●●●●●
Level 5
5 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a quadrilateral.
9.4 cm
112°
41°
63°
A
B
C
D
A
B
=
9.4
AB = 9.4
A
B
=
9.4
cm \qquad angle
A
B
C
=
112
°
ABC = 112°
A
B
C
=
112°
\qquad angle
C
A
D
=
41
°
CAD = 41°
C
A
D
=
41°
\qquad angle
A
C
D
=
63
°
ACD = 63°
A
C
D
=
63°
The area of triangle
A
B
C
ABC
A
B
C
is
38
38
38
cm²
Calculate the area of triangle
A
C
D
ACD
A
C
D
.
Give your answer correct to 3 significant figures.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
A
B
C
D
E
F
G
H
ABCDEFGH
A
B
C
D
E
F
G
H
is a cuboid.
A
B
C
D
E
F
G
H
A
C
=
7.5
AC = 7.5
A
C
=
7.5
cm \qquad
A
G
=
15
AG = 15
A
G
=
15
cm
Work out the size of the angle between
A
G
AG
A
G
and the plane
A
B
C
D
ABCD
A
B
C
D
.
(2 marks)
●●●●●
Level 5
2 marks
Start
→
Mark as done
A
B
C
D
E
F
G
H
ABCDEFGH
A
B
C
D
E
F
G
H
is a cuboid.
12 cm
34°
49°
A
B
C
D
E
F
G
H
A
B
=
12
AB = 12
A
B
=
12
cm \qquad angle
B
A
C
=
34
°
BAC = 34°
B
A
C
=
34°
\qquad angle
G
B
C
=
49
°
GBC = 49°
GB
C
=
49°
Work out the size of the angle between
A
G
AG
A
G
and the plane
A
B
C
D
ABCD
A
B
C
D
.
Give your answer correct to the nearest degree.
(4 marks)
●●●●●
Level 5
4 marks
Start
→