An observer wishes to determine the height of a tower. he takes sights at the top of the tower form a and b, which are 50 feet apart, at the same elevation on a direct line with the tower. the vertical angle point a is 30 degrees and at point b is 40 degrees. what is the height of the tower?

Vertical angle from A to the top of the tower: 30°

Horizontal distance from A to the base of the tower: 50 + x

Call h the height of the tower

ratio: tan 30 = h / (50+x) => 50 + x = h / tan30 => x = h / tan30 - 50    (1)

Vertical angle from B to the top of the tower: 40°

Horizontal distance from B to the base of the tower: x

ratio: tan 40 = h / x  => x = h / tan40    ...(2)

Then (1) and (2) are equal => h / tan40 = h/tan30 - 50 =>

h/tan30 - h/tan40 = 50

1,7321h - 1,1918h = 50

0.5403h = 50

h = 50/0.5403 = 92.54

92.54 ft
 

 

The variables should add up to equal 1