Cambridge IGCSE Maths (0580) · Topic 6: Trigonometry · 6.2
Right-Angled Trigonometry questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
In a right-angled triangle the hypotenuse is \(10\) cm and one angle is \(32°\).
Find the side opposite the \(32°\) angle, correct to 3 significant figures.
Answer: \(5.30\) cm
In a right-angled triangle one angle is \(50°\) and the side adjacent to it is \(7\) cm.
Find the side opposite the \(50°\) angle, correct to 3 significant figures.
Answer: \(8.34\) cm
In a right-angled triangle, one angle is \(35^\circ\) and the hypotenuse is 12 cm. Find the side opposite the \(35^\circ\) angle. Give your answer correct to 3 significant figures.
Answer: \(6.88\) cm
In a right-angled triangle the hypotenuse is \(9\) cm and the side opposite angle \(x\) is \(5\) cm.
Find \(x\), correct to 1 decimal place.
Answer: \(33.7°\)
In a right-angled triangle one angle is \(40°\) and the side adjacent to it is \(12\) cm.
Find the hypotenuse, correct to 3 significant figures.
Answer: \(15.7\) cm
A straight ramp rises 5 m over a horizontal distance of 12 m.
(a) Find the length of the ramp.
(b) Write down the tangent of the angle the ramp makes with the horizontal, as a fraction.
Answer: (a) \(13\) m (b) \(\frac{5}{12}\)
In a right-angled triangle, the sides next to the right angle are 5.2 cm and 8.1 cm. Find the angle opposite the 5.2 cm side. Give your answer correct to 1 decimal place.
Answer: \(32.7^\circ\)
A ship sails \(8\) km due north and then \(6\) km due east.
(a) How far is it from its starting point?
(b) Find the bearing of the ship from its starting point, correct to 1 decimal place.
Answer: (a) \(10\) km (b) \(036.9°\)
Extended content, for Papers 2 and 4. Core students can skip these.
From a point on level ground \(25\) m from the foot of a tower, the angle of elevation of the top of the tower is \(38°\).
Find the height of the tower, correct to 3 significant figures.
Answer: \(19.5\) m
From the top of a cliff \(80\) m high, the angle of depression of a boat is \(14°\).
How far is the boat from the foot of the cliff? Give your answer correct to 3 significant figures.
Answer: \(321\) m
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Right-Angled Trigonometry is on both tiers (syllabus 6.2), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
In the 0580 practice for topic 6 (Trigonometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.
IGCSE Math Revision