Answer :
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:
[tex]AB = 720 \frac{feet}{minute} \times 5 \text{minute} = 3600 feet[/tex]
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,
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
Here, opposite = BC = x
hypotenuse = AB = 3600 feet
Thus, we get,
[tex]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[/tex]
Thus the depth of sun after 5 minutes is 809.82 feet
