Question

the captain of a boat knows that the lighthouse on the coast is 200 feet tall. he measures the angle of elevation to the top of the lighthouse to be 2 degrees. how far is the boat from the coast? round to the nearest hundredth of a foot.

Answer 1

The boat is 5727.25ft far from the coast

Answer 2

The boat is 5727.25ft far from the coast

Explanation:

Refer the figure given.

We need to find how far is the boat from the coast = AB

Angle of elevation = 2°

The lighthouse on the coast is 200 feet tall, AC = 200 ft

We have

`tan2=(AC)/(AB)=(200)/(AB)\\\\AB=(200)/(tan2)=5727.25ft`

The boat is 5727.25ft far from the coast