Approximate the height of the tower..

Question

From a point P on level ground, the angle of elevation of the top of a tower is 29°20'. From a point 24.0 meters closer to the tower and on the same line with P and the base of the tower, the angle of elevation of the top is 57°30'. Approximate the height of the tower. (Round your answer to the nearest tenth.)

 

*Please give correct answer.. I need to check the answer i got. Thank you!


=___m

Answer 1

Let L = the original distance from the base of the tower and H = the height of the tower.

 

 

 

tan(29°20') = H/L     [1]

 

 

tan(57°30') = H/(L - 24.0)     [2]

 

 

 

Solving for L in [1] and substituting it in [2]:

 

L = H/tan(29°20')

 

 

[H/tan(29°20') - 24.0]tan(57°30') = H

 

 

 

Solving for H:

 

H[tan(57°30')/tan(29°20') - 1] = 24.0 tan(57°30')

 

 

H = 24.0 tan(57°30') / [tan(57°30')/tan(29°20') - 1] = 21.0 m = H

 

 

L = 37.4 m