Question

find x.
8 ft.
10 ft.
x = feet
submit

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 of length \(a\) and \(b\) and hypotenuse of length \(c\), \(a^{2}+b^{2}=c^{2}\). In this triangle, the hypotenuse \(c = 10\) ft, one leg \(a = 8\) ft and the other leg \(b=x\) ft.

Step2: Substitute values into the formula

Substitute \(a = 8\), \(c = 10\) into the Pythagorean theorem: \(8^{2}+x^{2}=10^{2}\)

Step3: Simplify the equation

Calculate \(8^{2}=64\) and \(10^{2}=100\). So the equation becomes \(64 + x^{2}=100\)

Step4: Solve for \(x^{2}\)

Subtract 64 from both sides of the equation: \(x^{2}=100 - 64=36\)

Step5: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents a length, we take the positive square root. So \(x=\sqrt{36}=6\)

Answer:

6