Question

A submarine dives at an angle of 13 degrees to the surface of the water. The submarine travels at a speed of 720 feet per minute. About how deep is the sun after 5 minutes?

Answer 1

The depth of sun after 5 minutes is 809.82 feet

Solution:

A submarine dives at an angle of 13 degrees to the surface of the water

The submarine travels at a speed of 720 feet per minute

The figure is attached below

ACB is a right angled triangle

AB is the distance between surafce of water and submarine

BC is the depth of submarine

Let "x" be the depth of sun after 5 minutes

Therefore, distance between submarine and surface of water is:

$AB = 720 \frac{feet}{minute} \times 5 \text{minute} = 3600 feet$

Submarine dives at an angle of 13 degrees to the surface of the water

Therefore, angle A = 13 degrees

Now we have to find BC

By definition of sine,

$sin \theta = \frac{opposite}{hypotenuse}$

Here, opposite = BC = x

hypotenuse = AB = 3600 feet

Thus, we get,

$sin \theta = \frac{BC}{AB}\\\\sin \theta = \frac{x}{3600}\\\\sin 13 = \frac{x}{3600}\\\\0.2249 = \frac{x}{3600}\\\\x = 3600 \times 0.2249\\\\x = 809.82$

Thus the depth of sun after 5 minutes is 809.82 feet