Syllabus Edition

First teaching 2023

First exams 2025

|

Right-Angled Triangles - Pythagoras & Trigonometry (CIE IGCSE Maths: Extended)

Exam Questions

3 hours45 questions
1a
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2 marks

q13-paper4-spec-2025-cie-igcse-further-maths

The diagram shows a quadrilateral, A B C D, formed from two triangles, A B C and A C D.
A B C is a right-angled triangle.

Calculate angle B A C.

Angle B A C = ..............................................

1b
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3 marks

Calculate the shortest distance from D to A C.

.......................................... cm

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2
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3 marks

cie-igcse-2020-march-p2-tz2-q7a
The diagram shows a right-angled triangle.

Calculate the perimeter.


............................................ cm

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3
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2 marks

cie-igcse-2019-may-june-1-q7

The diagram shows a right-angled triangle.

Calculate the value of x.
 

x = ............................................

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4
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2 marks

UsCFLVj9_cie-icse-2018-may-jun-1-7

Calculate the length of AC.


AC = ........................................ cm

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5
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2 marks

cie-igcse-2018-march-p2-16

Calculate AC.


AC = .................................... m

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6
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3 marks

Here is a right-angled triangle.

q2-easy-4-10-right-angled-triangle-edexcel-gcse-maths

Work out the length of A C.
Give your answer correct to 1 decimal place.

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7
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3 marks

q3-easy-4-10-right-angled-triangle-edexcel-gcse-maths

L M N spaceis a right-angled triangle.
M N space= 9.6 cm.
L M= 6.4 cm.

Calculate the size of the angle marked x degree.
Give your answer correct to 1 decimal place.

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8
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3 marks

q5-easy-4-10-right-angled-triangle-edexcel-gcse-maths

P Q R spaceis a right-angled triangle.
P R = 17 cm
P Q space= 25 cm

Work out the size of angle R P Q.
Give your answer correct to 1 decimal place.

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9
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2 marks

A B C spaceis a right-angled triangle.

q6-easy-4-10-right-angled-triangle-edexcel-gcse-maths

Calculate the length of A B.
Give your answer correct to 3 significant figures.

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10
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2 marks

P Q R spaceis a right-angled triangle.

q7-easy-4-10-right-angled-triangle-edexcel-gcse-maths

Work out the size of the angle marked x.
Give your answer correct to 1 decimal place.

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11
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2 marks

cie-igcse-2020-oct-nov-p4-tz1-q4b

ABDF is a parallelogram and BCDE  is a straight line.
AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.

Calculate the height, h, of the parallelogram.


 

h space equals ........................................... cm

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12a
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3 marks

cie-igcse-2018-oct-nov-p4-tz1-q5

The diagram shows a prism with length 18 cm and volume 253.8 cm3.
The cross-section of the prism is a right-angled triangle with base 6 cm and height h cm.

Show that the value of h is 4.7 .

 

12b
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2 marks

Calculate the value of x.
 

x = ...............................................

12c
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6 marks

Calculate the total surface area of the prism.
 

........................................ cm2

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13
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5 marks

h0KYsqUX_cie-igcse-2018-oct-nov-p4-tz1-q10a

The diagram shows a circle, centre O.
The straight line ABC is a tangent to the circle at B.
OB = 8 cm, AB = 15 cm and BC = 22.4 cm.
AO crosses the circle at X and OC crosses the circle at Y.
 
Calculate angle XOY.
 

Angle XOY = .............................................

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14
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2 marks

cie-igcse-2018-oct-nov-p4-tz3-q8a

In the diagram, AB and CD are parallel.
AD and BC intersect at right angles at the point X.
AB = 10 cm, CD = 5 cm, AX = 8 cm and BX = 6 cm.

Calculate angle XAB.


 

Angle XAB = ..............................................

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15
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5 marks

Here is part of a field.

q3-medium-4-10-right-angled-triangle-edexcel-gcse-maths

This part of the field is in the shape of a trapezium.
A farmer wants to put a fence all the way around the edge of this part of the field.

The farmer has 50m of fence.

Does he have enough fence?
You must show all your working.

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16
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4 marks

The diagram shows a rectangular framework.

q4-medium-4-10-right-angled-triangle-edexcel-gcse-maths

The framework is made from 5 metal rods.
The metal rods have a weight of 0.9 kg per metre.

Work out the total weight of the framework.
Give your answer, in kg, correct to 3 significant figures.

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17
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3 marks

The diagram shows a rectangle and a diagonal of the rectangle.

q4-4-ma1-2hr-qp-jan20-paper2-igcse-maths

Work out the length of the diagonal of the rectangle.
Give your answer correct to 1 decimal place.

.....................cm

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1
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3 marks

cie-igcse-2018-may-jun-2-p2-q16
The diagram shows a circle, centre O.
AB is a chord of length 12 cm.
M is the mid-point of AB and OM = 4.5 cm.

Calculate the radius of the circle.

.......................................... cm

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2
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4 marks

A B C spaceis an isosceles triangle.

q9-medium-4-10-right-angled-triangle-edexcel-gcse-maths

Work out the area of the triangle.
Give your answer correct to 3 significant figures.

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3
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3 marks

q11-medium-4-10-right-angled-triangle-edexcel-gcse-maths

Calculate the length of P R.
Give your answer correct to 3 significant figures.

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4a
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2 marks

A B C spaceis a right-angled triangle.

q7a-medium-4-10-right-angled-triangle-edexcel-gcse-maths

Work out the size of angle A B C.
Give your answer correct to 1 decimal place.

4b
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1 mark

The length of the side space A B spaceis reduced by 1 cm.

The length of the side space B C spaceis still 7 cm.
Angle space A C B spaceis still 90°

Will the value of cosspace A B C spaceincrease or decrease?
You must give a reason for your answer.

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5
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2 marks

A solid metal cone has radius 1.65 cm and slant height 4.70 cm.

Find the angle the slant height makes with the base of the cone.

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6
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2 marks

cie-igcse-2020-specimen-p4-q9a

The diagram shows a trapezium A B C D.
A B is parallel to D C.
A B space equals space 55 space straight m, B D space equals space 70 space straight m, angle A B D space equals space 40 degree and angle B C D space equals space 32 degree.

Calculate the shortest distance from A to B D.


 ............................................ m

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7
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2 marks

The straight line A C has equation y equals 4 x plus 5.

Calculate the acute angle between A C and the x-axis.

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8
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2 marks

In this question, all measurements are in metres.

cie-igcse-2018-may-jun-2-p4-q7
The diagram shows a right-angled triangle.

Given that x equals 3.82 to 3 significant figures, calculate the smallest angle of the triangle.

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9a
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4 marks

cie-igcse-2018-may-jun-3-p4-q6a
In the pentagon A B C D E, angle A C B = angle A E D = 90°.
Triangle A C D is equilateral with side length 12 cm.
D E = B C = 6 cm.

Calculate angle B A E.


Angle
B A E = ...............................................

9b
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2 marks

Calculate A B.

A B = ......................................... cm
9c
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3 marks

Calculate A E.

A E = ......................................... cm

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1
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5 marks

cie-igcse-2020-may-june-p2-tz1-q13

C lies on a circle with diameter A D.
B lies on A C and E lies on A D such that B E is parallel to C D.
A B = 21 cm, C D = 18 cm and B E = 13.5 cm.

Work out the radius of the circle.


............................................ cm

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2
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3 marks

Point A has co-ordinates (1, 0) and point B has co-ordinates (2, 5).

Calculate the angle between the line AB and the x-axis.

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3
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4 marks

A square, with sides of length x cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.

The area of the circle is 49 cm2.

Work out the value of x.
Give your answer correct to 3 significant figures.

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4
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5 marks

Here is triangle A B D.

q10-paper1h-jan2019-edexcel-igcse-maths

The point C lies on B D.

A D space equals space 13 cm space space space space space space B C space equals space 8 cm space space space space space space space angle space A D B space equals space 90 degree space space space space space space angle space C A D space equals space 20 degree

Calculate the size of angle B A C.
Give your answer correct to 1 decimal place.

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5
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3 marks

cie-igcse-2020-may-june-p4-tz1-q7

The diagram shows the positions of three points A, B and C in a field.

Calculate the shortest distance from point B to A C.

............................................. m

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6
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6 marks

cie-igcse-2020-may-jun-p4-tz2-q5

The diagram shows a field ABCD.
The bearing of B from A is 140°. 
C is due east of B and D is due north of C.
AB = 400m, BC = 350m and CD = 450m.

Calculate the distance from D to A.
 

 ............................................. m

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7
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2 marks

cie-igcse-2019-oct-nov-p4-tz1-q5a

The angle B A C is 82.8 degree correct to 3 significant figures.

D is the point on AC that is nearest to B.

Calculate the distance from D to A.

................................................ m

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8
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4 marks

cie-igcse-2020-may-jun-p4-tz1-q3

The diagram shows a field ABCDE.

Calculate the perimeter of the field ABCDE.
 

................................................ m

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9
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3 marks

cie-igcse-2019-may-jun-p4-tz3-q9a

In the diagram, B C is a vertical wall standing on horizontal ground A B.
A C = 76.7 m.
D is the point on A B where A D = 58 m.
The angle of elevation of C from A is 26°.
The angle of elevation of C from D is 72°.

Calculate B D.
 

B D = .......................................... m

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