Trigonometry-25

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The angle of depression of a boat B from the top K of cliff HK, 300 meters high, is 40⁰.
Find the distance of the boat from the foot H of the cliff.

Solution: Let the required distance BH be equal to x meters. HK is the cliff and angle LKB is the angle

of depression of B from K. Then

∠KBH = ∠LKB [alt ∠s, LM || BH]

Therefore, ∠BKH = 90⁰ - 40⁰ = 50⁰

From triangle BKH, we get

x/300 = tan 50⁰

Therefore, x = 300 X tan 50⁰ = 300 X 1.1918 = 357.54

= 358 m correct to the nearest meter.