Question

An 18-foot ribbon is attached to the top of a pole and is located on the ground 10 feet awayfrom the base of the pole. Suppose Mateo has a second ribbon that will be located anadditional 23 feet away past that point.Find the measure length a.a10 ft18 ftx23 fte

Answer 1

We have the following triangle as stated in the question:

And we need to find the measure of length a.

1. To find it, we can observe that:

2. And we have the following information from this right triangle:

• Length of the hypotenuse = 18ft

,

• Length of one of the legs 10ft

,

• The side, a, corresponds to the other leg of the right triangle

3. Therefore, we can apply the Pythagorean Theorem to find the length of leg a as follows:

$a^2+10^2=18^2$

4. Then we have to solve the equation for, a, as follows:

$\begin{gathered} a^2+10^2-10^2=18^2-10^2 \\ \\ a^2=18^2-10^2 \end{gathered}$

5. Now, we have to extract the square root to both sides of the equation:

$\sqrt{a^2}=\sqrt{18^2-10^2}=\sqrt{224}$

6. To simplify the result, we need to find the factors of 224:

Then the factors are:

$\begin{gathered} 224=2^5*7 \\ \\ \sqrt{224}=\sqrt{2^4*2*7}=2^2\sqrt{14} \\ \\ a=4\sqrt{14} \end{gathered}$

Therefore, in summary, the measure length a i