Question 41
TrigonometryThe pilot of an aeroplane, flying 10km above the ground in the direction of a landmark, views the landmark to have angles of depression of 35° and 55°. Find the distance between the two points of observation.
- A.10(sin35° − sin55°)
- B.10(cos35° − cos55°)
- C.10(tan35° − tan 55°)
- D.10(cot 35° − cot 55°)
Show the answer and explanation
Answer: D (10(cot 35° − cot 55°))
Explanation
At height 10km, the horizontal distance to the landmark is 10 cot θ for a depression angle θ. The two positions are 10 cot 35° and 10 cot 55° away, so the distance between them is 10(cot 35° − cot 55°).