A surveyor has determined that a mountain is h 2330 ft high

A surveyor has determined that a mountain is h = 2330 ft high. From the top of the mountain be measures the angles of depression to two landmarks at the base of the mountain and finds them to be 43degreee and c = (Observe that these are same as the angles of elevation from the landmarks as shown in the figure below.) The angle between the lines of sight to the landmarks is 68degree. Calculate the distance between the two landmarks.

Solution

tan(42degree) = A/2330
A = 2097.9 ft
and
tan(39 degree) = B/2330
B = 1886.8 ft
these are the distances from the reference point
and these make an angle of 68°
so we have two sides and the included angle which calls for the Law of Cosines
D = sqrt(2097.9 ^2 + 1886.8^2 - 2 (2097.9 ) (1886.8) cos(68degree)) = 2235 ft between the landmarks