Question

a shark is swimming 28 ft below sea level. if the angle of depression from a boat on the water to the shark is 19°, what is the horizontal distance (in feet) between the boat and the shark?

Explanation:

Step1: Identify the triangle type

This is a right triangle problem where the vertical side (opposite to the angle of depression) is 28 ft, and we need to find the horizontal side (adjacent to the angle of depression). We can use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 19^\circ$, opposite side $= 28$ ft, and adjacent side is the horizontal distance $d$ we need to find.

Step2: Set up the tangent equation

$\tan(19^\circ) = \frac{28}{d}$

Step3: Solve for $d$

$d = \frac{28}{\tan(19^\circ)}$
First, calculate $\tan(19^\circ) \approx 0.3443$
Then, $d = \frac{28}{0.3443} \approx 81.3$ (rounded to one decimal place)

Answer:

The horizontal distance between the boat and the shark is approximately $\boxed{81.3}$ feet.