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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.
Solution
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.
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