SOLUTION: The angle of elevation of the top of a tower as observed from A is 30 degrees. At point B, 20m from A the angle of elevation of the top of the tower is 42 degrees. Assume A, B and

Algebra ->  Trigonometry-basics -> SOLUTION: The angle of elevation of the top of a tower as observed from A is 30 degrees. At point B, 20m from A the angle of elevation of the top of the tower is 42 degrees. Assume A, B and       Log On


   

Question 1187820: The angle of elevation of the top of a tower as observed from A is 30 degrees. At point B, 20m from A the angle of elevation of the top of the tower is 42 degrees. Assume A, B and the base of the tower lies on the same horizontal plane. Find the height of the tower. Find the distance from the base of the tower to the point B.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The angle of elevation of the top of a tower as observed from A is 30 degrees.
At point B, 20m from A the angle of elevation of the top of the tower is 42 degrees.
Assume A, B and the base of the tower lies on the same horizontal plane.
Find the height of the tower.
Find the distance from the base of the tower to the point B.
:
Draw this out as two right triangles with a common height
Let x = dist from the base of the tower to angle B
then
(x+20) = dist from the base of the tower to angle A
let h = height of the tower
:
Two tangent equations
side opposite is the height and sides adjacent are x and (x+20)
Tan(30) = h%2F%28%28x%2B20%29%29
h = tan(30)*(x+20)
h = .57735x + 11.547
and
Tan(42) = h%2Fx
h = tan(42)x
h = .9x
:
h = h therefore
.9x = .57735x + 11.547
.9x - .57735x = 11.547
.323x = 11.547
x = 11.547/.323
x = 35.75 m is the distance from the base of the tower to B
then
35.75 + 20 = 55.75 m is the distance to A
:
Find the height of the tower using
Tan(42) = h%2F35.75
h = tan(42) * 35.75
h = 32.19 meter is the height of the tower
:
Check the height using
Tan(30) = h%2F55.75
h = 32.19 meters