Question

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.

Answer 1

Answer:

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