Two surveyors, Joe and Alice, are 240 meters apart on a riverbank. Each sights a flagpole on the opposite bank. The angle from the pole to Joe (vertex) to Alice is 63 degrees. The angle from the pole to Alice(vertex)to Joe is 54 degrees. How far are Joe and Alice from the pole?

Answer 1

C(3rd angle) = 180 - 63 - 54 = 63deg.
If 2 angles(63deg) of a triangle are =
the sides opp. these angles are =.
Therefore, Alice's dist. from pole =
240m.

Using the Law of Sines,

d / sin54 = 240 / sin63,
d = 240sin54 / sin63 = 218m. = Joe's
dist. from pole.