Your town is building a wind generator to create electricity for your school. The builder wants your geometry class to make sure that the guy wires are placed so that the tower is secure. By safety guidelines, the distance along the ground from the tower to the guy wire's connection with the ground should be between 50% to 75% of the height of the guy wire's connection with the tower.

a. The tower is 64 feet tall. The builders plan to have the distance along the ground from the tower to the guy wire's connection with the ground be 60% of the height of the tower. How far apart are the tower and the ground connection of the wire? 

b. How long will a guy wire need to be that is attached 60 feet above the ground? 

c. How long will a guy wire need to be that is attached 30 feet above the ground? 

d. Find the angle of elevation of each wire. Are the right triangles formed by the ground, tower, and wires congruent, similar, or neither? Explain. 

e. Explain which trigonometric ratios you used to solve the problem.