SOLUTION: In the figure, a person standing at point A notices that the angle of elevation to the top of the antenna is 47° 30'. A second person standing 38.0 feet farther from the antenna t

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Question 1195556: In the figure, a person standing at point A notices that the angle of elevation to the top of the antenna is 47° 30'. A second person standing 38.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 44° 10'. How far is the person at A from the base of the antenna? (Round your answer to the nearest whole number.)
https://www.webassign.net/mcktrig6/2-4-023.gif -picture of figure
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In the figure, a person standing at point A notices that the angle of elevation to the top of the antenna is 47° 30'.
A second person standing 38.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 44° 10'.
How far is the person at A from the base of the antenna? (Round your answer to the nearest whole number.)
:
Change 47 degrees 30 min to 47.5 degrees (divide the min by 60)
Change 44 degrees 10 min to 44.17 degrees
:
Write a tangent equation for each right triangle
tan(47.5) = h%2Fx
h = tan(47.5)x
and
tan(44.17) = h%2F%28%28x%2B38%29%29
h = tan(44.17)(x+3)
:
h=h, therefore we can find x
tan(47.5)x = tan(44.17)(x+38)
tan(47.5)x = tan(44.17)x + 36.9
tan(47.5)x - tan(44.17)x = 36.9
.12x = 36.9
x = 36.9/.12
x = 307.5 ~ 308 ft, A is from the base of the tower