Question

A pole 12 feet tall is used to support a guy wire for a tower, which runs from the tower

to a metal stake in the ground. After placing the pole, Xin measures the distance from
the pole to the stake and from the pole to the tower, as shown in the diagram below.
Find the length of the guy wire, to the nearest foot.

Answer 1

122ft

Explanation:

(Note that this is just a logical guess, I do not remember learning how to do this)

We are given the length of the pole and the length of the guy wire after the pole. This gives us a right angle triangle where we know two of the sides. We can the other two sides into the Pythagorean theorem to solve for the diagonal side

recall:

`{a}^(2) + {b}^(2) = {c}^(2)`

plugged in 12ft and 2ft we get:

`{(12)}^(2) + {(2)}^(2) = 148`

to solve for the diagonal side we take the square root of 148

`√(148) = 12.17`

so now we know that 12.17 ft of wire is equivalent to 2 feet on the ground.

`(12.17ft \: wire)/(2 \: ft \: ground)`

We have a total of 20 feet, so we multiply this proportion by 20:

`(12.17)/(2) * 20 = 121.7`

we are asked to give to the nearest foot so we round up to 122ft