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Browse Pythagoras & right-angled trigonometry
54 questions at your level
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Level 1
Level 2
Level 3
Level 4
Level 5
Pythagoras' theorem
24 questions
Lesson
Not started
Mark as done
A circle has centre
O
O
O
and radius
25
25
25
cm.
A
B
AB
A
B
is a chord of length
30
30
30
cm.
(a)
Work out the distance from
O
O
O
to the chord
A
B
AB
A
B
.
(b)
M
M
M
is the midpoint of
A
B
AB
A
B
, and the line
O
M
OM
O
M
is extended to meet the circle at
N
N
N
. Work out the length of
M
N
MN
M
N
.
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Level 4
5 marks
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→
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The diagram shows a cuboid measuring
10
10
10
cm by
6
6
6
cm by
8
8
8
cm.
10 cm
6 cm
8 cm
Diagram NOT accurately drawn
Work out the length of the longest diagonal of the cuboid. Give your answer correct to 1 decimal place.
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Level 4
4 marks
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→
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An isosceles triangle has a base of
16
16
16
cm and two equal sides of
17
17
17
cm.
Work out the
area
of the triangle.
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Level 4
4 marks
Start
→
Mark as done
The four vertices of rectangle
P
Q
R
S
PQRS
P
QR
S
lie on a circle, centre
O
O
O
.
11 cm
6.5 cm
P
Q
R
S
O
P
Q
=
11
PQ = 11
P
Q
=
11
cm
Q
R
=
6.5
\qquad QR = 6.5
QR
=
6.5
cm
Work out the circumference of the circle.
Give your answer correct to 3 significant figures.
(4 marks)
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Level 4
4 marks
Start
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Right-angled trigonometry (SOHCAHTOA)
31 questions
Lesson
Not started
Mark as done
A ship sails
9
9
9
km due East from
P
P
P
to
Q
Q
Q
, and then
5
5
5
km due North from
Q
Q
Q
to
R
R
R
.
9 km
5 km
P
Q
R
N
Diagram NOT accurately drawn
Work out the bearing of
R
R
R
from
P
P
P
. Give your answer correct to the nearest degree.
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Level 4
3 marks
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→
Mark as done
A helicopter flies
8
8
8
km from
A
A
A
on a bearing of
125
°
125°
125°
to reach
B
B
B
.
(a)
Work out how far East of
A
A
A
the point
B
B
B
is. Give your answer correct to 3 significant figures.
(b)
Work out how far South of
A
A
A
the point
B
B
B
is. Give your answer correct to 3 significant figures.
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Level 4
4 marks
Start
→
Mark as done
A phone mast
M
M
M
is
7.4
7.4
7.4
km due West and
3.9
3.9
3.9
km due North of a house
H
H
H
.
(a)
Work out the distance
H
M
HM
H
M
. Give your answer correct to 3 significant figures.
(b)
Work out the bearing of
M
M
M
from
H
H
H
. Give your answer correct to the nearest degree.
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Level 4
5 marks
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→
Mark as done
The diagram shows a right-angled triangle.
7.5 cm
x
34°
Diagram NOT accurately drawn
Work out the length of
x
x
x
. Give your answer correct to 1 decimal place.
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Level 4
3 marks
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→
Mark as done
The diagram shows a right-angled triangle.
5 cm
x
60°
Diagram NOT accurately drawn
(a)
Write down the exact value of
tan
60
°
\tan 60°
tan
60°
.
(b)
Work out the exact length of
x
x
x
, giving your answer in the form
a
3
a\sqrt{3}
a
3
.
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Level 4
3 marks
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→
Mark as done
The diagram shows a right-angled triangle.
x
11 cm
52°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Give your answer correct to 3 significant figures.
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●
Level 4
3 marks
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→
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(a)
Write down the exact value of
sin
30
°
\sin 30°
sin
30°
(b)
A right-angled triangle has hypotenuse
14
14
14
cm, and one of its angles is
30
°
30°
30°
.
Using your answer to part (a), work out the
exact
length of the side opposite the
30
°
30°
30°
angle.
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Level 4
3 marks
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→
Mark as done
A ship leaves a harbour
H
H
H
and sails
8
8
8
km on a bearing of
060
°
060°
060°
to a point
P
P
P
. It then sails
5
5
5
km on a bearing of
150
°
150°
150°
to a point
Q
Q
Q
.
(a)
Work out the distance
H
Q
HQ
H
Q
. Give your answer correct to 3 significant figures. (3 marks)
(b)
Work out the bearing of
Q
Q
Q
from
H
H
H
. Give your answer correct to the nearest degree. (2 marks)
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Level 4
5 marks
Start
→
Mark as done
(a)
A right-angled triangle has hypotenuse
8
8
8
cm and one angle of
60
°
60°
60°
. Work out the exact length of the side opposite the
60
°
60°
60°
angle. [2]
(b)
Another right-angled triangle has hypotenuse
6
2
6\sqrt{2}
6
2
cm and one angle of
45
°
45°
45°
. Work out the exact length of the side adjacent to the
45
°
45°
45°
angle. [2]
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Level 4
4 marks
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→
Mark as done
The diagram shows two right-angled triangles.
2x + 3
15
10
x + 3
a
b
All lengths are measured in centimetres.
Given that
sin
a
=
tan
b
\sin a = \tan b
sin
a
=
tan
b
work out the value of
x
x
x
.
(3 marks)
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Level 4
3 marks
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→
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P
Q
R
PQR
P
QR
is a triangle.
S
S
S
is a point on
Q
R
QR
QR
.
9.6 cm
47°
29°
P
Q
R
S
P
Q
=
9.6
PQ = 9.6
P
Q
=
9.6
cm \qquad angle
P
Q
S
=
47
°
PQS = 47°
P
QS
=
47°
\qquad angle
P
R
S
=
29
°
PRS = 29°
P
R
S
=
29°
Work out the length of
P
R
PR
P
R
.
Give your answer correct to 1 decimal place.
(3 marks)
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Level 4
3 marks
Start
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