Q) As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 60°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use 3 = 1.73)

Ans:

As observed from the top trigonometry applications important Questions

Let’s consider AB is the tower and 2 ship are at C & D.

In Δ ABC,

tan 600 =   \frac{AB}{AC}

√3 = \frac{75}{AC}

AC = 25 √3

In Δ ABD,

tan 300 =  \frac{AB}{AD}

\frac{1}{\sqrt3} = \frac{75}{d + 25\sqrt3}

d + 25√3 = 75 √3

d = 50 √3 = 50 x 1.73 = 86.5

Therefore, the distance between the two ships is 86.5 m

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