Hello, ccdalamp!
This type of problem can be solved without the Law of Sines,
. . but it requires more work.
A cable to the top of a tower makes an angle of 35° with the level ground.
At a point 100 yards closer to the tower, the angle of elevation to the top
of the tower is 59°. .Estimate the length of the cable. Code:
* D
* * |
* * |
L * * |
* * |t
* * |
* 35° * 59° |
* - - - - - - * - - - - - - *
A 100 B x C
In the diagram: .
In right triangle . [1]
In right triangle . [2]
Equate [1] and [2]: .
. . Solve for
In right triangle
Therefore: . yards.