posted by Brooke .
from a window 35 meters high, the angle of depression to the top of a nearby street light is 55 degrees. The angle of depression to the base of the streetlight is 57.8. How tall is the streetlight?
Start with the 57.8 degree angle and the 35 feet opposite the angle
tan 57.8 = 35/d
where d is the horizontal distance from the building to the light
d = 35 / tan 58.8 = 21.2 m
so then you have a second triangle up top with 55 degree angle, (35-h) opposite, and 21.2 adjacent so
tan 55 = (35-h)/21.2
35 - h = 30.3
h = 4.7 meters (about 15 feet)