Question

what is the value of x in the right triangle shown below? 13 feet 5 feet x 23 feet 8 feet 12 feet 18 feet

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a\) and \(b\) are legs. Here, \(a = 5\), \(c = 13\), \(b = x\). So \(5^2 + x^2 = 13^2\).

Step2: Simplify the equation

Calculate \(5^2 = 25\) and \(13^2 = 169\). The equation becomes \(25 + x^2 = 169\).

Step3: Solve for \(x^2\)

Subtract 25 from both sides: \(x^2 = 169 - 25 = 144\).

Step4: Find \(x\)

Take square root: \(x = \sqrt{144} = 12\).

Answer:

12 feet