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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
Level 2
Level 3
Level 4
Level 5
Pythagoras' theorem
24 questions
Lesson
Not started
Mark as done
The diagram shows a circle with centre
O
O
O
and radius
13
13
13
cm.
A
B
AB
A
B
is a chord of length
24
24
24
cm.
24 cm
13 cm
A
B
O
Diagram NOT accurately drawn
Work out the distance from the centre
O
O
O
to the chord
A
B
AB
A
B
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
P
A
PA
P
A
is a tangent to a circle with centre
O
O
O
and radius
8
8
8
cm. The point
A
A
A
is where the tangent touches the circle.
O
P
=
17
OP = 17
O
P
=
17
cm.
Work out the length of
P
A
PA
P
A
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle with hypotenuse
25
25
25
cm.
24 cm
y
25 cm
Diagram NOT accurately drawn
(a)
Work out the length of
y
y
y
.
(b)
Work out the distance between the points
(
−
3
,
2
)
(-3, 2)
(
−
3
,
2
)
and
(
5
,
8
)
(5, 8)
(
5
,
8
)
.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
A ladder leans against a vertical wall. The foot of the ladder is
1.4
1.4
1.4
m from the base of the wall, and the ladder reaches
4.2
4.2
4.2
m up the wall.
4.2 m
1.4 m
ladder
Diagram NOT accurately drawn
Work out the length of the ladder. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
A triangle has sides of length
8
8
8
cm,
15
15
15
cm and
17
17
17
cm. Show that this triangle is right-angled.
(b)
A different triangle has sides of length
7
7
7
cm,
9
9
9
cm and
12
12
12
cm. Determine whether this triangle is right-angled. You must show your working.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A right-angled triangle has hypotenuse
41
41
41
cm and one shorter side of length
40
40
40
cm.
Work out the length of the third side.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
A
A
A
is the point
(
1
,
2
)
(1, 2)
(
1
,
2
)
and
B
B
B
is the point
(
7
,
10
)
(7, 10)
(
7
,
10
)
.
Work out the length of the line segment
A
B
AB
A
B
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A solid cone has base radius
6
6
6
cm and slant height
10
10
10
cm.
6 cm
10 cm
Diagram NOT accurately drawn
Volume of a cone
=
1
3
π
r
2
h
= \dfrac{1}{3}\pi r^2 h
=
3
1
π
r
2
h
Work out the volume of the cone.
Give your answer correct to 3 significant figures. (4 marks)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows trapezium
P
Q
R
S
PQRS
P
QR
S
.
9 cm
6 cm
P
Q
R
S
P
Q
=
9
PQ = 9
P
Q
=
9
cm
P
S
=
6
PS = 6
P
S
=
6
cm
The trapezium has an area of
72
72
72
cm²
Work out the perimeter of the trapezium.
Give your answer correct to
3
3
3
significant figures.
(5 marks)
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●●
Level 3
5 marks
Start
→
Right-angled trigonometry (SOHCAHTOA)
31 questions
Lesson
Not started
Mark as done
The diagram shows a right-angled triangle.
x
9.6 cm
38°
Diagram NOT accurately drawn
Work out the length of
x
x
x
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
9.2 cm
6.5 cm
θ
Diagram NOT accurately drawn
Work out the size of the angle marked
θ
\theta
θ
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
x
12 cm
38°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Give your answer correct to 3 significant figures.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
9 cm
14 cm
x
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
x
12 cm
30°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. (2 marks)
●●●
●●
Level 3
2 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
7.2 cm
y
41°
Diagram NOT accurately drawn
Work out the value of
y
y
y
. Give your answer correct to 3 significant figures. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a right-angled triangle.
4.5 cm
7.2 cm
θ
Diagram NOT accurately drawn
Work out the size of angle
θ
\theta
θ
. Give your answer correct to 1 decimal place. (3 marks)
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Level 3
3 marks
Start
→