Guy wire???

Question

A guy wire 1000 feet long is attached to the top of a tower. When pulled taut it makes a 43 degree angle with the ground. How tall is the tower? How far away from the base of the tower does the wire hit the ground?

Answer 1

Visualize this guy wire, guy; it's the hypotenuse (if you believe that it's possible to have a wire hypotenuse of length one thousand feet, pulled taut to be a strait line segment!).  The tower's height is tfeet, and there's an acute angle 43^o between the horizontal ground and the hypotenuse. Elementary Trigonometry: sin 43 = t / 1000

so t = 1000 sin 43 and the rest is up to you and your trusty calculator (be sure it's in Degree Mode).

Answer 2

When you draw your right triangle

hypotenuse = wire length = 1000 ft

The vertical building = length x

The horizontal distance from building base to wire bottom = y

 

Building height:

Sine function:  sin 43 = opposite/hypotenuse = x/1000

                      x = 1000 sin 43

                      x ≅ 682 ft

 

Distance from tower base to wire:

Cosine function:  cos 43 = adjacent/hypotenuse = y/1000

                         y = 1000 cos 43

                         y ≅ 731.35 ft