Question

Find the angle of depression from the top of a lighthouse, 260 feet above water to a ship that's 270 feet offshore?

A.87.840
B.46.08 °
C. 43.92 °
D.92.160

Answer 1

Answer: OPTION C.

Explanation:

Observe the triangle ABC attached.

Notice that the angle of depression is represented with
`\alpha`.

Knowing that the top of a lighthouse is 260 feet above water and the ship is 270 feet offshore, you can find the value of
`\alpha` by using arctangent:

`\alpha= arctan((opposite)/(adjacent))`

In this case you can identify that:

`opposite=260\\adjacent=270`

Therefore, substuting values into
`\alpha= arctan((opposite)/(adjacent))`, you get that the angle of depression is:

`\alpha= arctan((260)/(270))\\\\\alpha=43.92\°`