A 20 ft. wire stretches from the top of a light pole diagonally to the ground. The light pole is 12 feet high. What is the angle the wire makes with the ground?

The ground makes a right angle with the light pole. Drawing a triangle, the wire (20 ft) is the hypotenuse because it is opposite of the right angle. We are referring to the angle that the wire makes to the ground and the light pole is opposite of that angle, and we know that it is 12 ft tall.

Since we are looking for the angle's measure, we use the inverse trigonometric function. But first, we need to figure out which function we are using. We are referring to the opposite side and the hypotenuse, so that is sine (Soh Cah Toa = sine = opposite/hypotenuse). Since the light pole is the opposite side and the wire is the hypotenuse, we substitute that into our equation.

Sin = 12/20 = 0.6.

Now, we must use the inverse to find the measure of the angle. [tex]sin^{-1} (0.6) = 36.8699[/tex]

So the angle that the wire makes with the ground = [tex]approx. 36.87[/tex]

We can check our work by finding the measure of the opposite angle. [tex]Sin(36.87) = 12/20[/tex]

Multiply by 20 on both sides

[tex]Sin(36.87)*20 = 12[/tex]

Put that into the calculator and we'll get approximately 12.