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natulia [17]
3 years ago
12

From the top of a lighthouse 280 feet tall, to keep her spot a ship in distress at an angle of depression of 18°. How far is the

boat from shore(The base of the lighthouse) round to the nearest foot
Mathematics
1 answer:
solong [7]3 years ago
4 0

Given:

Height of the lighthouse = 280 feet

The angle of depression from the top of the lighthouse to a ship = 18°.

To find:

The distance between boat and shore.

Solution:

Draw a diagram by using the given information.

In a right angle triangle,

\tan \theta=\dfrac{Perpendicular}{Base}

In triangle ABC,

\tan C=\dfrac{AB}{BC}

\tan 18^\circ=\dfrac{280}{BC}

BC=\dfrac{280}{\tan 18^\circ}

Using a calculator, we get

BC=\dfrac{280}{0.3249}

BC=861.80363...

BC\approx 862

Therefore, the boat is 862 feet away from shore.

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