I am assuming you were supposed to be using Pythagorean theorem. So I will help you solve it that way. As you know Pythagorean theorem needs a right angle and the three sites.Because the line is a tangential wine that means that it is perpendicular to a radius; therefore, that’s the right angle. r and 120 are legs, a & b. The hypotenuse is 80 plus what? How long? 80+ r.
Pythagorean Theorem:
A^2 + b^2 = c^2
120^2 + r^2 = (80 + r)^2
(120)(120) + r^2 = (r + 80)(r +80))
14400+ r^2 = r^2 + 160r + 6400
8000=160r
R=5 ft.
