Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Shape and Space 3
17 practice questions
Practice questions
11–17 of 17
Question 11
2 marks · Normal
Answer and check →A triangle has a tangent ratio of 1.0 at one of its angles. Write down the value of that angle to the nearest degree.
Question 12
3 marks · Normal
Answer and see the solution →At a certain time of day, the shadow of a vertical post measures 4.2 m. The angle of elevation of the Sun is 68°.
Calculate the height of the post. Give your answer correct to 2 decimal places.
Question 13
4 marks · Normal
Answer and see the solution →A man is standing on a riverbank. Across the river is a tree. The width of the river is 18 m. The angle of elevation from the man’s feet to the top of the tree is 25°. The tree is vertical and the ground is level.
(a)[3 marks]Calculate the height of the tree. Give your answer correct to 1 decimal place.
(b)[1 mark]Explain why the triangle used in your calculation is a right-angled triangle.
Question 14
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 15
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 16
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 17
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.