Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Shape and Space 3
17 practice questions
Practice questions
1–4 of 4 · Hard
Question 1
4 marks · Hard
Answer and see the solution →A ladder leans against a vertical wall and reaches a point 7.2 m above the ground. The foot of the ladder is 2.7 m from the base of the wall.
Calculate the angle, to the nearest degree, that the ladder makes with the ground.
(a)[4 marks]Find the angle described and show your full working.
(b)[0 marks](c)[0 marks]Question 2
5 marks · Hard
Answer and see the solution →(a)[4 marks]The diagram below shows triangle PQR. PQ = 9.0 cm, PR = 6.2 cm and angle QPR = 48°.
Triangle PQR with PQ = 9.0 cm, PR = 6.2 cm, angle QPR = 48°. Calculate the length QR, giving your answer correct to 3 significant figures.
(b)[1 mark]Write down which side in triangle PQR is the hypotenuse relative to angle QPR.
Question 3
3 marks · Hard
Answer and see the solution →A helicopter hovers above a straight road. From a point 120 m along the road from the point directly below the helicopter, the angle of elevation to the helicopter is 28°.
Calculate the height of the helicopter above the ground. Give your answer to the nearest metre.
Question 4
4 marks · Hard
Answer and see the solution →Explain, using step-by-step reasoning and a diagram, how you would use Pythagoras’ Theorem to check whether a triangle with sides 10 cm, 16 cm, and 18 cm is a right-angled triangle.