SOLUTION: The angle of elevation of the top of a building from point A on the ground is 24.1 degrees . From point B, which is 44.5 ft closer, the angle of elevation is 38.1 degrees. what is

Algebra ->  Trigonometry-basics -> SOLUTION: The angle of elevation of the top of a building from point A on the ground is 24.1 degrees . From point B, which is 44.5 ft closer, the angle of elevation is 38.1 degrees. what is       Log On


   

Question 1147782: The angle of elevation of the top of a building from point A on the ground is 24.1 degrees . From point B, which is 44.5 ft closer, the angle of elevation is 38.1 degrees. what is the height of the building
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The angle of elevation of the top of a building from point A on the ground is 24.1 degrees .
From point B, which is 44.5 ft closer, the angle of elevation is 38.1 degrees. what is the height of the building
:
let h = the height of the building
Let's treat this as two right triangles with the same opposite side(bldg height)
let x = the distance from B = x
then
(x+44.5) = A's distance to the building
1st triangle
tan(24.1) = h%2F%28x%2B44.1%29
tan(24.1)(x+44.1) = h
2nd triangle
tan(38.1) = h%2Fx
tan(38.1)x = h
h=h therefore
tan(38.1)x = tan(24.1)(x+44.5)
Find the tan of the angles
.7841x = .4473(x+44.5)
.7841x - .4473x + 19.9
.7841x - .4473x = 19.9
.3368x = 19.9
x = 19.9/.3368
x = 59.1 ft
Find the height of the building using the closer triangle
h = tan(38.1)*59.1
h = 46.33 ft
:
Check the height using the other triangle
h = tan(24.1)(59.1+44.5)
h = 46.34 ft