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Right-Angled Triangles: Pythagoras & Trigonometry (Cambridge O Level Maths): Exam Questions

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Right-Angled Triangles: Pythagoras & Trigonometry

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1a
Sme Calculator2 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 = ..............................................

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1b
Sme Calculator3 marks

Calculate the shortest distance from D to A C.

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

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2
Sme Calculator2 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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3
Sme Calculator3 marks

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

Calculate the perimeter.


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

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4
Sme Calculator2 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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5a
Sme Calculator3 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 .

 

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5b
Sme Calculator2 marks

Calculate the value of x.
 

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

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5c
Sme Calculator6 marks

Calculate the total surface area of the prism.
 

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

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6
Sme Calculator5 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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7
Sme Calculator2 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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8
Sme Calculator2 marks

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

Calculate the length of AC.


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

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9
Sme Calculator2 marks

cie-igcse-2018-march-p2-16

Calculate AC.


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

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10
Sme Calculator3 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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11
Sme Calculator5 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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12
Sme Calculator4 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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13
Sme Calculator3 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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14
Sme Calculator3 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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15
Sme Calculator2 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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16
Sme Calculator2 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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17
Sme Calculator3 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
Sme Calculator2 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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2
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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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3
Sme Calculator2 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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4
Sme Calculator3 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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5
Sme Calculator2 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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6a
Sme Calculator4 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 = ...............................................

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6b
Sme Calculator2 marks

Calculate A B.

A B = ......................................... cm

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6c
Sme Calculator3 marks

Calculate A E.

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

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7
Sme Calculator4 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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8
Sme Calculator3 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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9a
Sme Calculator2 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.

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9b
Sme Calculator1 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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10
Sme Calculator6 marks

A B C D spaceis a trapezium with space B C spaceparallel to A D

q4a-june-2018-4024-2-cambridge-o-level-maths-d

E is the point on A D such that space B E spaceis perpendicular to A D.
B D with hat on top A = 55°, space A E space= 7 cm, space B E space= 18 cm and space B C space= 9 cm

Calculate

i)
B Â E,

B Â E= ....................[2]

ii)
the area of the trapezium A B C D.

.......................cm2 [4]

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1
Sme Calculator5 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
Sme Calculator3 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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3
Sme Calculator6 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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4
Sme Calculator2 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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5
Sme Calculator4 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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6
Sme Calculator3 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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7
Sme Calculator3 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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8
Sme Calculator4 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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9
Sme Calculator5 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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