Cambridge IGCSE · Mathematics (0580)

Right-angled triangles: Practice Questions

4 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Right-angled triangles.

9 questions19 marksFree, no account

Question 1

1 mark

In triangle \(XYZ\), the angle \(\angle Y = 90^{\circ}\). The side lengths are \(XY = 7\) cm and \(YZ = 10\) cm.
Calculate the size of angle \(\angle YXZ\), giving your answer correct to 1 decimal place.

Question 2

1 mark

A vertical flagpole stands on level ground. From a point on the ground 18.5 m from the base of the flagpole, the angle of elevation to the top of the flagpole is \(38^\circ\).

Calculate the height of the flagpole, giving your answer correct to 3 significant figures.

Question 3

1 mark

A surveyor at a point A on horizontal ground measures the angle of elevation of the top of a vertical tower as \(25^{\circ}\). He then walks \(40\) m closer to the tower to point B, where the angle of elevation becomes \(40^{\circ}\).
Find the height of the tower, correct to 1 decimal place.

Question 4

1 mark

In a right-angled triangle \(ABC\), the side opposite to angle \(BAC\) is \(BC = 5 \text{ cm}\) and the hypotenuse is \(AC = 12 \text{ cm}\). Calculate the size of angle \(BAC\) correct to 1 decimal place.

Question 5

2 marks

A right-angled triangle has a hypotenuse of length \(13\text{ cm}\) and one leg of length \(5\text{ cm}\). Calculate the length of the third side.

Write your answer out first, then check it against the worked solution.

Question 6

3 marks

A ship sails \(12\text{ km}\) North and then \(16\text{ km}\) East. Calculate the three-figure bearing of the ship from its starting point, to the nearest degree.

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

Two vertical poles of heights \(9\text{ m}\) and \(14\text{ m}\) stand on level ground. The distance between the bases of the two poles is \(12\text{ m}\). Calculate the straight-line distance between the tops of the two poles.

Write your answer out first, then check it against the worked solution.

Question 8

2 marks

A vertical flagpole stands on horizontal ground. From a point on the ground \(25\text{ m}\) away from the base of the flagpole, the angle of elevation to the top of the flagpole is \(26^\circ\).
Calculate the height of the flagpole. Give your answer correct to 3 significant figures.

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

A person is standing at the top of a cliff of height \(45\text{ m}\) above sea level. From the top of the cliff, they observe a boat at sea.

(a) The angle of depression from the top of the cliff to the boat is \(19^\circ\). Calculate the direct distance from the observer to the boat. Give your answer correct to 3 significant figures.

(b) Calculate the horizontal distance from the base of the cliff to the boat. Give your answer correct to 3 significant figures.

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, marked as you go.