3 years ago

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Mathematics

1 answer:

zalisa [80]3 years ago

8 0

It is showing growth.

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An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. To the nearest foot, how far is the boa

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Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = $7^{\circ}$

$\angle CAB = \angle DCA = 7^{\circ}$ [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

$\tan (\theta) = \frac{Opposite side}{Adjacent Base}$

$\tan (\angle CAB) = \frac{BC}{AB}$

Here, BC = 50 foot and $\angle CAB =7^{\circ}$

then;

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Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'

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