CAIE IGCSE Mathematics C6.2 Right-angled triangles Question Bank

Practise solving right-angled triangle diagrams by choosing sine, cosine, tangent or Pythagoras from the labelled sides and angles.

Exam points

choose sin, cos or tan from the labelled sides to calculate a missing angle or length
use Pythagoras when two sides of a right-angled triangle determine the third side
combine trigonometry and Pythagoras across joined right-angled triangles in a diagram

Covered syllabus points

C6.2.1 Know and use the sine, cosine and tangent ratios for acute angles in C6.2.2 Solve problems in two dimensions using Pythagoras’ theorem and

[Maximum number: 6]

The diagram shows a circle, centre O, radius 11 cm. C, F, G and H are points on the circumference of the circle.
The line AD touches the circle at C and is parallel to the line EG. B is a point on AD and angle $A B O=140^{\circ}$ .

(a)

Show that $BC=13.11\text{ cm}$ , correct to 2 decimal places.

[ 3 ]

180-140 or 90- their (b)(ii)
$\tan(180-140)=\frac{11}{BC}$ oe
$[BC=]13.109\ldots$

(b)

Calculate BH.

BH= ___ cm

[ 3 ]

6.11 or 6.112 to 6.114
M1 for $OB^{2}=13.11^{2}+11^{2}$ .
A1 for 17.1 or 17.11 or 17.112 to 17.114.
OR
M1 for $\frac{11}{\sin40}$ oe.
A1 for 17.1 or 17.11... or 17.112 to 17.113.

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Covered syllabus points

C6.2 Right-angled triangles question 1

Question (a)

Question (b)