Shape and Space 3
3 marks · HardA 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.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
64 m (±1)
Common mistakes: Using sine or cosine instead of tangent; Incorrect ratio (e.g. 120 × tan 28° rather than 120 ÷ tan 28°)
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Chooses correct trigonometric relation (tan)
M2 · 1 mark · Sets up calculation h = 120 × tan 28°; (follow-through)
A1 · 1 mark · Gives a correct height to the nearest metre (64 m). (follow-through)
Worked solution
Let h be the height of the helicopter. Using the tangent ratio:
Height to the nearest metre: 64 m.