Question

A shark is swimming 42 feet below sea level. If the angle of depression from a boat on the water to the shark is 23°, what is the horizontal distance between the boat and the shark? Show your work to receive full credit. Round to the nearest hundredth if necessary. ​

Answer 1

BC ≈ 98.95 feet

Explanation:

From the figure attached,

A shark is swimming 42 feet below sea level at point A and a boat on the water is at point C.

If the angle of depression from the coat to shark is 23°,

tan(23°) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

tan(23°) =
`(AB)/(BC)`

BC =
`\frac{AB}{\text{tan}(23)}`

BC =
`\frac{42}{\text{tan}23}`

BC = 98.947

BC ≈ 98.95 feet