Question

a boat is heading towards a lighthouse, whose beacon light is 117 feet above the water. the boats crew measures the angle of elevation to tye beacon 3. what is the ships horizontal distnace from the lighthouse( and the shore)? round your answer to the nearest hundreth of a foot if necessary.

Answer 1

So,

We could draw the situation of the problem as follows:

We want to find the horizontal distance, which we will call "x".

To find it, we could use the trigonometric ratio: tan(a).

This ratio relations the opposite side of the angle given (a) and its adjacent side. So, we could write:

`\tan (3)=(117)/(x)`

Now, if we solve for x:

`x=(117)/(\tan (3))`

This is, x = 2232.49 ft