SOLUTION: At distance x from the base of a building, the angle of elevation to top of the building is 19 degrees. The angle of elevation is 39 degrees if you walk 13 ft closer to the build

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Question 1136454: At distance x from the base of a building, the angle of elevation to top of the building is 19 degrees. The angle of elevation is 39 degrees if you walk 13 ft closer to the building. There is a 10 ft antenna on top of the building. Find the height from ground to the top of the antenna.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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At distance x from the base of a building, the angle of elevation to top of the building is 19 degrees.
The angle of elevation is 39 degrees if you walk 13 ft closer to the building.
There is a 10 ft antenna on top of the building.
Find the height from ground to the top of the antenna.
:
let h = the height of the building, a right triangle is formed
tan(19) = h%2Fx
and
tan(39) = h%2F%28%28x-13%29%29
Rearrange to
h = x*tan(19)
and
h = (x-13)*tan(39)
h = h, therefore
tan(39)*(x-13) = tan(19)*x
.8098x - 10.527 = .3443x
.8098x - .3443x = 10.527
.4655x = 10.527
x = 10.527%2F.4655
x = 22.614 ft
find h
h = tan(19) * 22.614
h = 7.785 ft is the height of he building
therefore
7.785 + 10 = 17.785 ft is the height of the antenna
:
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Check this, find the height of the building using the tan of 39 degrees
tan(39) * (22.614-13) = 7.785 ft also