Question

1. use the pythagorean theorem to find the unknown side length of the right triangle.

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let the unknown leg be \(a\), \(b = 24\space m\) and \(c=26\space m\). We need to solve for \(a\), so we can rearrange the formula to \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values into the formula

Substitute \(c = 26\) and \(b=24\) into the formula: \(a=\sqrt{26^{2}-24^{2}}\). First, calculate \(26^{2}=676\) and \(24^{2} = 576\). Then, \(26^{2}-24^{2}=676 - 576=100\).

Step3: Calculate the square root

Now, \(a=\sqrt{100}=10\).

Answer:

The unknown side length is \(10\space m\).