What angle does the guy wire make with the ground?

Question

A 112 meter guy wire is attached to the top of a 79 meter antenna and to a point on the ground. How far is the point on the ground from the antenna, and what angle does the guy wire make with the ground? (Round answers to 2 decimal places) 

 

Please Explain in Detail 

Answer 1

you have a right triangle

the vertical leg is 79 m and the hypotenuse is 112 m

use the Pythagorean Theorem

112²=79²+x² where x is the other leg  and the distance from the point on the ground to the antenna

12,544=6241+x²

12,544-6241=x²

x²=6303

x=79.39 m

to find the angle use sin=opposite/hypotenuse

sin(a)=79/112

sin(a)=0.705357

a≈44º51.5′

this answer makes sense because one leg is 79 m and the other leg is 79.39 m, so you almost have an isosceles right triangle which would make the two acute angles 45º each