Question

From a 200-foot observation tower on the beach, a man sights a whale in difficulty. The angle of depression of the whale is 7˚. How far is the whale from the shoreline?​

Answer 1

Given:

From a 200 ft tower, a man sees a whale

The angle of depression of the whale is 7°

To find:

The distance of the whale from the shoreline

Solution:

Referring to the figure attached below, we have

AB = 200 ft = height of the tower

∠ACB = 7° ...... [since the angle of depression is given as 7°]

BC = the distance of the whale from the shoreline

One of the relations of the trigonometric ratios of the triangle is,

$\boxed{tan\: \theta = \frac{Perpendicular}{Base} }$

here θ = 7°, AB = perpendicular and BC = base

Now, substituting the values of AB and θ, we get

tan 7° = $\frac{AB}{BC}$

⇒ 0.12278 = $\frac{200}{BC}$

⇒ BC = $\frac{200}{0.12278}$

⇒ BC = 1628.92 ft

Thus, the whale is 1628.92 ft far away from the shoreline.

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