A support wire is attached to a cell phone tower 75m high. The wire meets the ground at 57 degree angle. How long is the wire?

Answer 1

draw a right triangle

the vertical side (the tower) will be 75 m

the horizontal side is not needed

let x be the hypotenuse (the length of the wire)

the wire and the ground make a 57° angle

use the sine function

sin=opposite/hypotenuse

sin57°=75/x

x=75/sin57°

x=75/0.8386705

x=89.427254 m (round as needed)

the wire is 89.427254 m in length

Answer 2

Picture a right triangle with a right angle formed by a line segment that is vertical and one that is horizontal. The two segments meet at the lower left of your triangle. The height of the triangle is the height of the tower. The wire of unknown length is the hypotenuse of the triangle. The angle given, 57 degrees, is the angle at the lower right of yout triangle (the angle between the ground and the wire).

You can find the missing sides of a right triangle either by using the Pythagorean Theorem or by some trigonometry. Since we only know one side, we can't use Pythagorean Theorem.

Trigonometry means we can relate sides of a triangle to one or more of the angles in the right triangle. Here, if we look at the 57 degree angle, we know the side opposite, 75 meters, and want to know the hypotenuse. Which trig function relates opposite/hypotenuse to an angle? That's what you need to solve this. Your answer will be larger than 75 meters, by the way.