Question

find the length of the missing side. provide an answer accurate to the nearest tenth.
17 yards
36 yards

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 17\) and \(b\) (missing side) and hypotenuse \(c=36\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So, \(b^{2}=c^{2}-a^{2}\).
Substitute \(a = 17\) and \(c = 36\) into the formula: \(b^{2}=36^{2}-17^{2}\).
Calculate \(36^{2}=1296\) and \(17^{2}=289\). Then \(b^{2}=1296 - 289=1007\).

Step2: Solve for \(b\)

Take the square root of \(b^{2}\), \(b=\sqrt{1007}\).
Using a calculator, \(\sqrt{1007}\approx31.7\).

Answer:

\(31.7\) yards