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Pythagoras & right-angled trigonometry
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Browse Pythagoras & right-angled trigonometry
54 questions at your level
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Level 1
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Level 5
Pythagoras' theorem
24 questions
Lesson
Not started
Mark as done
A square has a diagonal of length
12
12
12
cm.
(a)
Work out the side length of the square. Give your answer correct to 3 significant figures.
(b)
Work out the
exact
area of the square.
●●●●●
Level 5
3 marks
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→
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
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→
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
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→
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
→
Mark as done
Ten identical regular octagons are joined together as shown in the diagram.
a
S
The octagons enclose the shape
S
S
S
.
Each side of each octagon has length
a
a
a
.
Find an expression, in terms of
a
a
a
, for the area of
S
S
S
.
Give your answer in the form
p
(
5
+
2
2
)
a
2
p(5 + 2\sqrt{2})a^2
p
(
5
+
2
2
)
a
2
where
p
p
p
is an integer.
You must show all your working.
(5 marks)
●●●●●
Level 5
5 marks
Start
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Right-angled trigonometry (SOHCAHTOA)
31 questions
Lesson
Not started
Mark as done
A yacht sails from
P
P
P
on a bearing of
070
°
070°
070°
for
12
12
12
km to reach
Q
Q
Q
. It then sails on a bearing of
160
°
160°
160°
for
9
9
9
km to reach
R
R
R
.
12 km
9 km
P
Q
R
N
N
Diagram NOT accurately drawn
(a)
Show that angle
P
Q
R
PQR
P
QR
is a right angle.
(b)
Work out the distance
P
R
PR
P
R
.
(c)
Work out the bearing of
R
R
R
from
P
P
P
. Give your answer correct to the nearest degree.
●●●●●
Level 5
7 marks
Start
→
Mark as done
A ship leaves a harbour
H
H
H
and sails
15
15
15
km on a bearing of
048
°
048°
048°
to a point
A
A
A
.
It then sails
25
25
25
km due South to a point
B
B
B
.
(a)
Work out the distance
H
B
HB
H
B
. Give your answer correct to 1 decimal place.
(b)
Work out the bearing of
B
B
B
from
H
H
H
. Give your answer correct to the nearest degree.
●●●●●
Level 5
7 marks
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→
Mark as done
Priya stands
45
45
45
m from the foot of a tower on level ground. From her eye, the angle of elevation of the top of the tower is
27
°
27°
27°
.
Priya's eyes are
1.6
1.6
1.6
m above the ground.
Work out the height of the tower. Give your answer correct to 1 decimal place.
●●●●●
Level 5
4 marks
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→
Mark as done
A boat is
130
130
130
m from the base of a vertical cliff of height
58
58
58
m.
Work out the angle of
depression
of the boat from the top of the cliff. Give your answer correct to 1 decimal place.
●●●●●
Level 5
3 marks
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→
Mark as done
P
Q
R
PQR
P
QR
is a right-angled triangle.
5.2 cm
7.4 cm
x
P
Q
R
P
Q
=
7.4
PQ = 7.4
P
Q
=
7.4
cm correct to the nearest mm.
Q
R
=
5.2
QR = 5.2
QR
=
5.2
cm correct to the nearest mm.
Calculate the upper bound for the size of the angle marked
x
x
x
.
You must show all your working.
(3 marks)
●●●●●
Level 5
3 marks
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→
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
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