a tree growing on a hillside casts a 102-foot shadow straight down the hill. Find the vertical height of the tree if, relative to the horizontal, the hill slopes 15.0 degrees and the angle of elevation of the sun is 62.0 degrees.

Answer 1

Draw a diagram.

vertical line for the tree, line OT
slanting line going down to the right at an angle if 15 degrees, of length 102, OS

Angle OTS is 62 degrees.
Angle TOS = 105 degrees.
so, angle OST = 13 degrees

Using the law of sines, the height of the tree, OT is given by

OT/sin13 = 102/sin62

OT = 102/.8829*.2250 = 26 feet