While visiting a memorial, a person approximated the angle of elevation to the top of the memorial to be 35º. After walking 255
ft closer, he guessed that the angle of elevation had increased by 17º. Approximate the height of the memorial, to the top of the memorial.
1 answer:
Draw a diagram to illustrate the problem as shown in the figure below.
Let h the height of the hill. =
At position A, the angle of elevation is 40°, and the horizontal distance to the foot of the hill is x.
By definition,
tan(40°) = h/x h = x tan40 = 0.8391x
(1)
At position B, Joe is (x - 450) ft from the foot of the hill. His angle of elevation is
40 + 18 = 58°.
By definition, tan(58°) = h/(x - 450)
h = (x - 450) tan(58°) = 1.6003(x-450)
h = 1.6003x - 720.135 (2)
Equate (1) and (2).
1.6003x - 720.135 = 0.8391x 0.7612x = 720.135
x = 946.0523
From (1), obtain
h = 0.8391*946.0523 = 793.8 ft
Answer: The height of the hill is approximately 794 ft (nearest integer)
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