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

Answer:

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

Step-by-step 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.

$tan\theta = \frac{Perpendicular}{Base}$

As shown in the figure given below.

Perpendicular = CB

Base = AC = 60 meters

$\theta = 12.5^{\circ}$

Put in the identity

$tan\ 12.5^{\circ} = \frac{CB}{AC}$

$tan\ 12.5^{\circ} = \frac{CB}{60}$

$tan\ 12.5^{\circ} = 0.22$

$tan\ 12.5^{\circ} = 0.22$

$0.22= \frac{CB}{60}$

CB = 60 × 0.22

CB = 13.2 meters

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