Similar Triangles Math Problem

Question

An airplane is from daejeon to busan.

1. From the plane, the angle of depression to busan is 8 degrees,
2. The air plane is in the air, and has traveled to a horizontal distance of 117 km.
3. From daejeon, the angle of elevation to the plane is 6 degrees.
4. Calculate the distance between daejeon and busan.

Answer 1

Triangle ABC, A on the left, B on top, C on the right.

The plane is at B.

Drop perpendicular from B to AC. The intersection is M.

Height h = MB

Angle A = 6, which forces angle ABM to be 84

AM = 117 is given

Per the given angle of depression, angle BMC is 82,

which forces angle C to be 8 degrees.

tan 6 = h/117

h = 117 * tan 6 = 12.29719552608416113845778476366

tan 8 = h/ MC

tan 8/1 = h * MC

h = MC* tan 8

h / tan 8 = MC

MC = h / tan 8 = 87.49909927165376845...

or just under 87.5

the distance between the 2 cities is then ABOUT 87.5+117 = 204.5