Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 3
104 practice questions
Topics covered
Practice questions
61–70 of 104
Question 61
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 62
2 marks · Normal
Answer and see the solution →Write down the value of tan 60°. Give your answer correct to 3 significant figures.
Question 63
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 64
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 65
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 66
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 67
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 68
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 69
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 70
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.