A wind storm caused a 64 ft pole to lean due easwt at an angle of 63.8 degrees to the ground. A 106 ft long guy wire is then attached to the top of the pole and anchored in the ground due west of the foot of the pole. How far from the foot of the pole is the guy wire anchored?

Answer 1

I see in the triangle the following:
obtuse angle: 180-63.8, opposite side 106ft, another side 64.

Law of sines to get the guy angle:
64/sinA=106/sin(180-63.8)
solve for angle A.
Then, knowing angle A, you can find the third angle at the top between the guywire and the flagpole.
law of sines:
SinA/64=SinThirdAngle/how far

solve for how far.