Assuming the tower is on level ground, how far from the base of the tower will the guywires be secured to the ground?

Question

The city of Austin is erecting a radio tower to boost cell phone coverage. They must install guy wires to support the tower in the wind. The guy-wires must attach to the tower at a point 56 feet above the base of the tower, and must form a 50° angle with the ground. Assuming that the tower is on level ground, how far from the base of the tower will the guy-wires be secured to the ground?

Answer 1

These types of problems are solved by drawing the diagram (right triangle) and then using the appropriate trig function. In this case, we are trying to find the adjacent side (length from base of the tower to the guy-wire) given an angle of 50° and opposite side is 56 feet (height above the base). In this case tan(50°)=56/x. Solve for x.