Two boats are sailing in the sea on the two opposite sides of a light house 50m high The angles of e...........

Quantitative Aptitude ( CCS) Trignometry

Two boats are sailing in the sea on the two opposite sides of a light house 50m high. The angles of elevation of the top of the light house observed from the ships are 30⁰ and 45⁰ respectively. Find the distance between the two ships.

136.6m

142.8m

150.4m

122.8m

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Explanation:

: Let AB is the light house of height 50m and the ships are at C & D making angles 30⁰ and 45⁰ respectively.
In ΔABC, tan 30⁰ = AB/BC
⇒ 1/√3 = 50/BC ⇒ BC = 50√3m
In ΔABD, tan 45⁰ = AB/BD
⇒ 1 = 50/BD = 50m
Heights & Distance Probs
∴ The distance between the ships = CD = CB + BD = 50√3 + 50 = 50 ( √3+1)m
= 50 × 2.732 = 136.6m