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?

Answer 1

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)