Application problem

Question

A guy wire 1266 feet long is attached to the top of a tower. When pulled taut, it touches level ground 848 feet from the base of the tower. What angle does the wire make with the ground? Express your answer using degree measure rounded to one decimal place. 

Answer 1

Hi Alex,

I've written up a solution, please take a look: https://imgur.com/a/2s0jomG

First, I started by drawing the problem out. Upon drawing it, I realized that for the angle that we're looking for (which I represent with the symbol Θ), we know the adjacent and the hypotenuse. Therefore, we'll be using cosine to solve this problem. The cosine of the angle is 848/1266. We can then take the inverse cosine of both sides. Inverse cosine of cosine of Θ is just Θ. Inverse cosine of 848/1266 is 47.9 (rounded to one decimal place).

Note: your calculator might show inverse cosine as "arc cos" instead of cos^-1

Hope this helps!

Answer 2

Start by drawing a picture.

"level ground" means that the base of the tower is at the same height as where the wire touches the ground. Your drawing will be a right triangle with a hypotenuse of 1266 feet.

The angle requested is found from the two known sides of the triangle: The hypotenuse, and the "adjacent" side to the angle.

Review your formulas to find the one that relates adjacent to hypotenuse.