Question

A guy wire to a tower makes a 71° angle with level ground. At a point 36 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is 36°. Find the length of the wire (to the nearest foot).

Answer 1

Explanation:

Draw a right triangle with the tower as the vertical leg, labeled h. From the base draw the horizontal leg which the right end makes a 71 angle of elevation with the top of the tower. Label this leg x. Extend this leg further to the right another 36 ft, the end of which makes a 37 angle of elevation with the top of the tower. You now have two right triangles to work with. Both triangles share a common vertical leg h. The 69 triangle has a horizontal leg x, and the 37 triangle has a horizontal leg ,x+36. The hypotenuse of the 69 triangle is the length of the guy wire, labeled L.