SOLUTION: A surveyor is sighting a building from a certain horizontal distance and found out that the angle of elevation to the top of the building 66degree. He moved 300ft farther and the

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Question 1145387: A surveyor is sighting a building from a certain horizontal distance and found out that the angle of elevation to the top of the building 66degree. He moved 300ft farther and the angle of elevation to the top of the building is 54degree.
what is the height of the building.?
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
First draw a right angled triangle ABC
Angle ABC = 90 degrees
Angle ACB = 66 degrees (given)
Extend BC out a distance to D. CD = 300 ft.
Draw a line from point D to point A
Angle ADC = 54 degrees.
If angle ACB = 66 deg. then angle ACD = 114 deg
This allows you to find angle DAC = 12 deg.
Using sine rule: a/sin A = d/sin D
300/sin (12) = x/ sin (54)
x = (300 * sin (54))/ sin (12)
x = 1167.35 ft
AC = 1167.35
Triangle ABC
AC = 1167.35
Angle c = 66 deg.
Using Sin = Oppos/Hyp : Sin (66) = Oppos/1167.35
Therefore Opposite (AB) = sin (66) * 1167.35 = 1066.43 feet (the height of the building.)
Hope this helps :-)