Question

A drone camera is used to shoot an object P from two different positions R and S along the same vertical line QRS. The angle of depression of the object P from these two positions is 35° and 60° respectively as shown in the diagram. If the distance of the object P from point Q is 50 metres, then find the distance between R and S correct to the nearest meter.

Answer 1

In ΔPQR,

tan 35° = `"QR"/"PQ" = "QR"/50`

∴ QR = 50 × tan 35°

= 50 × 0.7002

= 5 × 7.002

= 35.010 m

In ΔSQP,

tan 60° = `"SQ"/"PQ" = "SQ"/50`

∴ SQ = tan 60° × 50

= `50 sqrt3`

= 50 × 1.732

= 5 × 17.32

= 86.60

SR = SQ - QR

SR = 86.60 - 35.01

SR = 51.59 m

SR = 52 m

The distance between R and S is correct to the nearest 52 meters.