Question

A surveyor has determined that a mountain is
h = 2470
ft high. From the top of the mountain he measures the angles of depression to two landmarks at the base of the mountain and finds them to be 42° and
c = 39°.
(Observe that these are the 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 68°. Calculate the distance between the two landmarks. (Round your answer to the nearest integer.)

Answer 1

The solution for this problem is:
tan42 = A/2470 
A = tan 42 (2470)
A = 2224 ft 

and 

tan39 = B/2470 
B = tan 39 (2470)

B = 2000 ft 

These are the two 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(2224^2 + 2000^2 - 2 (2224) (2000) cos68) = 23669 ft between the landmarks