Question

find the value of x.
(right triangle with legs x and 15, hypotenuse 17)
x = ?

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 legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, the hypotenuse \(c = 17\), one leg \(b = 15\), and the other leg is \(x\).

Step2: Apply the Pythagorean theorem

We can rewrite the Pythagorean theorem to solve for \(x\). \(x^{2}+15^{2}=17^{2}\), so \(x^{2}=17^{2}-15^{2}\).
We know that \(17^{2}=289\) and \(15^{2}=225\). Then \(x^{2}=289 - 225=64\).

Step3: Solve for \(x\)

Taking the square root of both sides, since \(x\) represents the length of a side of a triangle (and length is non - negative), we have \(x=\sqrt{64}=8\).

Answer:

\(x = 8\)