Question

consider this right triangle.
find the exact length of the missing side.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 15\), \(b = 8\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).

Step2: Substitute values

Substitute \(a = 15\) and \(b = 8\) into the formula: \(c^{2}=15^{2}+8^{2}\).
Calculate \(15^{2}=225\) and \(8^{2}=64\). Then \(c^{2}=225 + 64\).

Step3: Simplify

\(c^{2}=289\).

Step4: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{289}\). Since \(c>0\) (length of a side), \(c = 17\).

Answer:

\(17\)