Question

Jack is standing on the top of the high diving board at the local pool which is 50 feet high. His friend Diane is

in the water. The direct (diagonal) distance from Jack to Diane is 75 feet. What is the angle of elevation from
Diane in the water to Jack on the diving board? Draw a picture that represents this situation and show all your
work to solve. Round your answer to the nearst WHOLE degree.

Answer 1

To find the angle of elevation from Diane in the water to Jack on the diving board, use the inverse tangent function with the height of the diving board and the distance between Jack and Diane as the opposite and adjacent sides, respectively. The angle of elevation is approximately 33.69°.

Step-by-step explanation:

To find the angle of elevation from Diane in the water to Jack on the diving board, we can use the inverse tangent function. The angle of elevation is the angle formed between the horizontal line and the line of sight from Diane to Jack. In this case, the opposite side is the height of the diving board (50 feet) and the adjacent side is the distance between Jack and Diane (75 feet).

So, the angle of elevation can be calculated using the formula: angle = arctan(opposite/adjacent). Plugging in the values, we get: angle = arctan(50/75) = arctan(2/3).

Using a calculator, we find that arctan(2/3) is approximately 33.69°. Therefore, the angle of elevation from Diane in the water to Jack on the diving board is approximately 33.69°.