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 = 38°.
The angle between the lines of sight to the landmarks is 68°. Calculate the distance between the two landmarks.

Answer 1

This is an image that is with the problem and these words were included in the description:
(Observe that these are the same as the angles of elevation from the landmarks as shown in the figure below.)

Answer 2

look at the third triangle and find two sides of it using the height and the angles provided

Answer 3

Using these:\[\frac{ 2470 }{ \sin38 }=\frac{ x }{\sin52}\] x=3161.4
\[\frac{ 2470 }{ \sin42 }=\frac{ x }{\sin16}\] x=1017.5

Then I found the angle in between to be 148.

Then using law of cosines I did:\[a^2 = 3161.4^2 + 1017.5^2 - 2(3161.4)(1017.5)\cos(148)\]
This resulted in a= 4060 (I only needed it as an integer)
This answer was incorrect. Where did I go wrong?

Answer 4

sin 32=....
sin 42=....

Answer 5

you could then find the two sides of the angle 68 and then use the cos law

Answer 6

I think I must not be following. I still got 4060.2 =/