Question

Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water, Marla's eye-level is 5.5 feet, and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff, tothe nearest foot?

Answer 1

Let us make a diagram to interpret the question

from the diagram above, we can make the right-angle triangle as follows

So we can use SOHCAHTOA to solve this. The opposite side to the angle 52 degrees is 45.5 ft, this is gotten by adding the height of the cliff to Maria's height from her feet to her eyes.

The adjacent side is d, that is the distance from the seal to the cliff, so we have

`\begin{gathered} TOA\text{ tan}\theta\text{ = }(opposite)/(adjacent) \\ tan52\degree=(45.5)/(d) \\ cross\text{ multiply, we have } \\ tan52\degree d=45.5 \\ d=(45.5)/(tan52) \\ d=35.54849 \end{gathered}`

Hence the answer is 36 foot to the nearest foot