A telephone pole is 56 feet tall. A wire that is 71 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the ground.

Question

Do not find the angle between the wire and the pole

Answer 1

For these types of questions I always find it useful to first start out by drawing a diagram. Unfortunately I am not able to upload mine, but I will do my best to describe the process.

We know that for the telephone pole it is going to be a straight line perpendicular with the ground. So, the telephone pole and the ground make a 90 degree angle. Now, there is a wire attached from the top of the pole to the ground. Imagine this as a diagonal line going from the top of the pole straight to the ground. Ok, so now the shape should start to look like a right triangle where the pole and ground form the 90 degree angle and the wire is the hypotenuse.

The angle we want is opposite of the pole, and is formed by the hypotenuse and the ground.

Recall the Sine Function: Sin(ø) = opposite/hypotenuse

We have both the opposite value = Pole of length 56 feet and the Hypotenuse = wire of length 71 feet

So, lets substitute these values back int our function: Sin(ø) = 56/71

to solve for ø, the angle, we need to take the inverse sine of both sides.

so, ø = Sin^-1(56/71)

Therefore, we should get the angle between the ground and the wire is equal to 52.07º