IGCSE Maths Right-Angled Trigonometry Questions and Answers
Right-Angled Trigonometry questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 5 worked examples first, then cover each solution and redo it yourself.
Pythagoras & right-angle trig (SOH-CAH-TOA): Finding missing sides and angles in right-angled triangles.
Trigonometry 1: SOH CAH TOA — finding an unknown side.
Trigonometry 2: SOH CAH TOA — finding an unknown angle.
Trigonometry 3: Sine rule for non-right-angled triangles.
Trigonometry 4: Cosine rule for non-right-angled triangles.
Right-Angled Trigonometry worked examples
Worked example 1: Finding a side with sine
A right-angled triangle has hypotenuse 10 cm and an angle of 35°. Find the side opposite the 35° angle.
Solution
Opposite and hypotenuse, so use sine: \(\sin35^\circ=\dfrac{x}{10}\).
\(x=10\sin35^\circ=5.735\ldots\)
\(x=5.74\) cm (3 s.f.).
Answer: 5.74 cm
Tip: Check your calculator is in degrees.
Worked example 2: Finding a side with tan
In a right-angled triangle the side adjacent to a \(40^\circ\) angle is 14 cm. Find the opposite side.
Solution
\(\tan40^\circ=\dfrac{x}{14}\).
\(x=14\tan40^\circ=11.7\) cm (3 s.f.).
Answer: 11.7 cm
Tip: Label O, A, H before choosing the ratio.
Worked example 3: Finding an angle
In a right-angled triangle the side opposite \(\theta\) is 7 cm and the adjacent side is 10 cm. Find \(\theta\).
Solution
\(\tan\theta=\dfrac{7}{10}\).
\(\theta=\tan^{-1}0.7=35.0^\circ\).
Answer: 35.0°
Tip: Use the inverse function to find an angle.
Worked example 4: Angle of elevation
From 12 m away on level ground, the angle of elevation of the top of a tree is \(28^\circ\). Find the height of the tree.
Solution
\(\tan28^\circ=\dfrac{h}{12}\).
\(h=12\tan28^\circ=6.38\) m.
Answer: 6.38 m
Tip: Elevation is measured up from the horizontal.
Worked example 5: Choosing the ratio
Triangle ABC has a right angle at C, AB = 9 cm and angle A = \(52^\circ\). Find BC.
Solution
AB is the hypotenuse and BC is opposite A, so use sine.
\(BC=9\sin52^\circ=7.09\) cm.
Answer: 7.09 cm
Tip: SOH CAH TOA.
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Which Edexcel IGCSE Maths papers test right-angled trigonometry?
Either Higher tier paper, 1H or 2H, can test right-angled trigonometry: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more right-angled trigonometry questions?
In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.
IGCSE Math Revision