EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Trigonometry 2
Trigonometry 2 · Angles and trigonometry · Lesson 7 of 7 · 11 marks · 25 minutes
Name Date
Answer all questions. Show your working. The calculator is allowed where the question says so.
Question 1 CALCULATOR [2 marks]
A right-angled triangle has hypotenuse 12 cm. The side adjacent to angle θ is 7 cm. Work out the size of angle θ. Give your answer to 1 decimal place.
Question 2 NON-CALCULATOR [2 marks]
A right-angled triangle has an angle of 60°. The hypotenuse is 14 cm. Work out the length of the side adjacent to the 60° angle.
Question 3 CALCULATOR [3 marks]
A lighthouse stands on the edge of a cliff. The top of the lighthouse is 80 m above sea level. The angle of depression from the top of the lighthouse to a boat is 25°. Work out the distance from the boat to the foot of the cliff. Give your answer to the nearest metre.
Question 4 CALCULATOR [4 marks]
A kite string is 30 m long and is pulled tight. The string makes an angle of 52° with the horizontal ground. The string is held 1.2 m above the ground. (a) Work out the height of the kite above the ground, to 1 decimal place. (b) The wind drops, and the kite falls to a height of 15 m, with the same length of string, still held 1.2 m above the ground. Work out the new angle between the string and the horizontal.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
cos θ= 7/12, so θ= cos ⁻¹(7/12) = 54.31…= 54.3°
▸ cos θ= 7/12 M1
▸ 54.3° A1
Question 2 [2 marks]
x = 14cos 60°= 14 × ½ = 7 cm
▸ 14cos 60° M1
▸ 7 cm A1
Question 3 [3 marks]
The angle of elevation of the top from the boat is also 25° (alternate angles). tan 25°= 80/d, so d = 80/(tan 25°) = 171.56…= 172 m.
▸ 25° placed at the boat, or the angle 65° at T found M1
▸ tan 25°= 80/d, or 80tan 65° M1
▸ 172 m A1
Question 4 [4 marks]
(a) 30sin 52°= 23.64…, plus 1.2 gives 24.8 m. (b) Height above the hand = 15 − 1.2 = 13.8 m. sin θ= 13.8/30, θ= sin ⁻¹(0.46) = 27.4°.
▸ (a) 30sin 52° M1
▸ (a) 24.8 m A1
▸ (b) sin θ= 13.8/30 M1
▸ (b) 27.4° A1