A communication tower is located at the top of a steep hill. The angle of inclination of the hill is 58 degrees. A guy wire is to be attached to the top of the tower and to the ground , 99 m downhill from the base of the tower. The angle ∠ BAC is 12 degrees.

Required:
Find the length of cable required for the guy wire.

Length of cable for guy wire = 153.39m

Step-by-step explanation:

I have attached a diagram that depicts this question.

From the diagram i attached,

Solving for angle B on the right triangle, we have;

∠B = 180° - 90° - 58°

∠B = 32°

Now, solving for angle B on the oblique triangle above the right triangle to give;

∠ABC = 180° - 32°

∠ABC = 148°

Solving for angle C on the oblique triangle

∠C = 180° - 148° - 12°

∠C = 20°

from the diagram b is the length of cable for the guy wire.

c is given as 99m

Thus,using sine rule, we have

c/sinC = b/sinB

So, 99/(sin20) = b/(sin 148)

b = 99(sin 148)/(sin20)

b = 153.39m

sine

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.