Suppose a person is standing on the top of a building and that she has an instrument that allows her to
measure angles of depression. There are two points that are 100 feet apart and lie on a straight line that is
perpendicular to the base of the building. Now suppose that she measures the angle of depression from the
top of the building to the closest point to be 35.5º and the angle of depression from the top of the
building to the furthest point to be 28.8º. Determine the height of the building. (Round your answer to the
nearest tenth of a foot.)
239.8 feet to the nearest tenth.
We have 2 right triangles one inside the other.
Let the height of the builing be x ft and the distance from foot of thebuiding to the closest point be y feet.
So we have the system:
tan 28.8 = x/(y + 100)
tan 35.5 = x/y
From second equation:
x = tan35.5 y
Sustituting in the first equation:
tan 28.8 = tan35.5 y / (y + 100)
tan35.5 y = tan 28.8 y + 100 tan 28.8
y(tan35.5 - tan28.8) = 100 tan 28.8
y = 100 tan 28.2 / (tan35.5 - tan28.8)
y = 336.16 ft
So x = height of the buiding = tan35.5 * 336.16
= 239.78 ft.