Apole is used to support an observation platform. the top of the pole is secured by two guy wires, one 18 and the other 21 feet in length. the 18 foot guy wire makes a 65± angle with the ground. how far apart, to the nearest foot, are the two wires at the points where they are anchored to the ground?

We can say that the top of the pole has a height ( h ). It is also a height of a triangle which sides are 18 and 21 ft and L  - the distance between the points where the two wires are anchored to the ground.
 L = x + y
 h = 18 · sin 65° = 18 · 0.9 = 16.31 ft
 x =  18 · cos 65° = 18 · 0.4226 = 7.60 ft
 y² = 21² - 16.31² = 441 - 266.1316 = 174.8684
 y = √ 174.8684 = 13.22
 L = 7.60 + 13.22 = 20.82 ft ≈ 21 ft.
21 ft.