Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Shape and Space 3
17 practice questions
Practice questions
1–8 of 8 · Normal
Question 1
3 marks · Normal
Answer and see the solution →A straight road runs up a hill at a constant angle with the horizontal. The road makes an angle of 18° with the horizontal and is 120 m long.
Calculate the height gained, correct to 3 significant figures.
Question 2
2 marks · Normal
Answer and see the solution →Write down the value of tan 60°. Give your answer correct to 3 significant figures.
Question 3
1 mark · Normal
Answer and see the solution →In the right-angled triangle below, which side is adjacent to angle ?
- A.AB
- B.BC
- C.AC
- D.CB
Question 4
4 marks · Normal
Answer and see the solution →A mobile phone mast is 48 m tall. From a point on level ground, the angle of elevation to the top of the mast is 40°.
(a)[3 marks]Calculate the distance from the point to the base of the mast, correct to 3 significant figures.
(b)[1 mark]Give a reason why the tangent ratio is suitable for this calculation.
Question 5
3 marks · Normal
Answer and see the solution →Work out the value of x in the triangle below. Give your answer correct to 3 significant figures.
PQ = 7 cm, angle R = 35°.
Question 6
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 7
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 8
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.