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प्रश्न
Draw the necessary diagram for this question.
A man on the top of a lighthouse observes the angles of depression of two ships on the opposite sides of the lighthouse as 30° and 50°, respectively. If the height of the lighthouse is 80 m, find the distance between the two ships. Give your answer correct to the nearest meter.
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उत्तर
From figure,
Let the top of the lighthouse be T, the base of the lighthouse be L, and the two ships be A and B.
Given,
The height of the lighthouse, TL, is 80 m.
The angles of depression are 30° and 50°.
These are equal to the alternate interior angles of elevation on the ships.
∠TBL = 50° and ∠TAL = 30°
In triangle TLA,
tan 30° = `"Perpendicular"/"Base"`
tan 30° = `(TL)/(LA)`
LA = `(TL)/(tan 30°)`
LA = `80/0.577`
LA = 138.65 m
In triangle TLB,
tan 50° = `"Perpendicular"/"Base"`
tan 50° = `(TL)/(LB)`
LB = `(TL)/(tan 50°)`
LB = `80/1.192`
LB = 67.11 m
Distance between ships = LA + LB
= 138.65 m + 67.11 m
= 205.76 m
Hence, the distance between the two ships is 206 m.
