Question

A ship's sonar finds that the angle of depression to a ship wrack on the bottom of the oceanis 12.5°. If a point on the ocean floor is 60 meters directly below the ship, how many meters is it from that point on the ocean floor to the wreck?

Answer 1

The 13.2 meters from that point on the ocean floor to the wreck.

Explanation:

As given

A ship's sonar finds that the angle of depression to a ship wrack on the bottom of the ocean is 12.5°.

If a point on the ocean floor is 60 meters.

Now by using the trigonometric identity.

`tan\theta = (Perpendicular)/(Base)`

As shown in the figure given below.

Perpendicular = CB

Base = AC = 60 meters

`\theta = 12.5^(\circ)`

Put in the identity

`tan\ 12.5^(\circ) = (CB)/(AC)`

`tan\ 12.5^(\circ) = (CB)/(60)`

`tan\ 12.5^(\circ) = 0.22`

`tan\ 12.5^(\circ) = 0.22`

`0.22= (CB)/(60)`

CB = 60 × 0.22

CB = 13.2 meters

Therefore the 13.2 meters from that point on the ocean floor to the wreck.