Question

While visiting a memorial, a person approximated the angle of elevation to the top of the memorial to be 34 degrees. After walking 253 ft closer, he guessed that the angle of elevation had increased by 14 degrees. Approximately, what is the height of the memorial to the top?

a) 438 ft
b) 541 ft
c) 624 ft
d) 732 ft

Answer 1

b) 541 ft. To solve this problem, we can use trigonometry and set up a right triangle. By using the tangent function and solving equations, we can determine the height of the memorial.

Step-by-step explanation:

To solve this problem, we can use trigonometry and set up a right triangle. Let's assume the height of the memorial is represented by h. The angle of elevation from the original position can be represented by 34 degrees, and from the closer position, it can be represented by 48 degrees.

By using the tangent function, we can set up two equations:

tan(34) = h/x, where x is the distance from the original position to the memorial

tan(48) = h/(x-253), where x-253 is the distance from the closer position to the memorial

Solving these equations will give us the value of h, which represents the height of the memorial. Calculating using these equations, we find that h is approximately 541 ft. Therefore, the height of the memorial to the top is approximately 541 ft.