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 (feet)/(minute) * 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 = (opposite)/(hypotenuse)`

Here, opposite = BC = x

hypotenuse = AB = 3600 feet

Thus, we get,

`sin \theta = (BC)/(AB)\\\\sin \theta = (x)/(3600)\\\\sin 13 = (x)/(3600)\\\\0.2249 = (x)/(3600)\\\\x = 3600 * 0.2249\\\\x = 809.82`

Thus the depth of sun after 5 minutes is 809.82 feet