Question

what is the length of the missing leg? if necessary, round to the nearest tenth.
b = feet

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 87\) ft and one leg \(a = 60\) ft, and we need to find the other leg \(b\).

Step2: Rearrange the Pythagorean theorem

We can rearrange the formula to solve for \(b\): \(b=\sqrt{c^{2}-a^{2}}\)

Step3: Substitute the values

Substitute \(c = 87\) and \(a = 60\) into the formula:
First, calculate \(c^{2}-a^{2}\):
\(c^{2}=87^{2}=7569\)
\(a^{2}=60^{2}=3600\)
Then \(c^{2}-a^{2}=7569 - 3600=3969\)

Step4: Take the square root

Now, find the square root of \(3969\): \(\sqrt{3969}=63\)

Answer:

\(b = 63\) feet