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.)

 

= ___ m

Answer 1

h = height of tower

x = short distance from tower

x + 24 = location of P

"

The drawing has two right triangles. For the small triangle

 

tan 51°30' = h/x

x tan 51°30' = h

 

For the large triangle

 

tan 29°20' = h/(x + 24)

(x + 24)tan 29°20' = h

 

x tan 51°30' = (x + h)tan 29°20'

x (1.234) = (24 + x)(0.554)

1.234x = 13.269 + 0.554x

0.68x = 13.269

x = 19.51

 

19.51 tan 51°30' = h

19.51 (1.234) = h

24.08 ≈ h

 

The tower is approximately 24 feet tall.