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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
=
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
→
The cosine rule
22 questions
Lesson
Not started
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
→
Area of a triangle & 3D trigonometry
21 questions
Lesson
Not started
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
→