A shark is swimming 28 feet below sea level. If the angle of depression from a boat on the water to the shark is 19 degrees, what is the horizontal distance between the boat and the shark? Round your answer to the nearest foot.

The horizontal distance between the boat and the shark is 82.35 feet.

Given that,

A shark is swimming 28 feet below sea level.

If the angle of depression from a boat on the water to the shark is 19 degrees,

We have to determine,

What is the horizontal distance between the boat and the shark?

According to the question,

A shark is swimming 28 feet below sea level.

If the angle of depression from a boat on the water to the shark is 19 degrees,

The angle of depression is the angle between the horizontal line from the observation point which is equal to,

Substitute all the values in the formula;

Hence, The required horizontal distance between the boat and the shark is 82.35 feet.

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The answer to your question is the horizontal distance = 81.32 ft

Step-by-step explanation:

Data

depth = 28 ft

angle = 19°

horizontal = ?

To solve this problem, use trigonometric functions. The trigonometric function that relates the opposite side and the adjacent side is the tangent.

       tan Ф = Opposite side/Adjacent side

-Solve for adjacent side

       Adjacent side = Opposite side / tanФ

-Substitution

       Adjacent side = 28 / tan 19

-Simplification

       Adjacent side = 28 / 0.3443

-Result

       Adjacent side = 81.32 ft

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50