Posted by john on Monday, June 10, 2013 at 7:06pm.
The angle of elevation from a point on the ground to the top of a tower is 37deg5'. The angle of elevation from a point 120 feet farther back from the
tower is 29deg5'. Find the height of the tower (to the nearest foot).

Trig  Reiny, Monday, June 10, 2013 at 8:29pm
did you make a sketch?
I have , top of tower  P , bottom of tower Q
closer point A
farther point B
In triangle PBA
angle B = 29°5'
angle BAP = 142°55'
angle BPA = 8°
AB = 120
by sine law:
PA/sin 29°5' = 120/sin 8°
PA = 419.1165
now triangle APQ is rightangled
use
sin 37°5' = PQ/PA
you finish it 
Trig  john, Monday, June 10, 2013 at 8:55pm
I got 263.

Trig  Reiny, Monday, June 10, 2013 at 11:36pm
I get 252.717 or 253