Question

1. a = 10 ft, b = 24 ft

Explanation:

Assuming this is a right - triangle problem where we need to find the hypotenuse \(c\) using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) (since \(a = 10\space ft\) and \(b=24\space ft\) are the legs of a right triangle).

Step 1: Recall the Pythagorean theorem

For a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the formula is \(c=\sqrt{a^{2}+b^{2}}\).

Step 2: Substitute the values of \(a\) and \(b\)

We know that \(a = 10\space ft\) and \(b = 24\space ft\). First, calculate \(a^{2}\) and \(b^{2}\):
\(a^{2}=(10)^{2}=100\) and \(b^{2}=(24)^{2} = 576\)
Then, find the sum of \(a^{2}\) and \(b^{2}\): \(a^{2}+b^{2}=100 + 576=676\)

Step 3: Calculate the square root of the sum

Now, find \(c\) by taking the square root of \(676\): \(c=\sqrt{676} = 26\space ft\)

Answer:

If we are finding the hypotenuse of a right - triangle with legs \(a = 10\space ft\) and \(b = 24\space ft\), the length of the hypotenuse \(c\) is \(26\space ft\).