Question

the hypotenuse of a right triangle measures 13 feet, and the base measures 6 feet. what is the measure of the height? 7 feet 11.5 feet 14.3 feet 19 feet

Explanation:

Step1: Apply Pythagorean theorem

Let the height be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 13\) (hypotenuse) and \(a = 6\) (base). So \(6^{2}+h^{2}=13^{2}\).

Step2: Simplify the equation

\(36+h^{2}=169\). Then \(h^{2}=169 - 36\).

Step3: Calculate \(h^{2}\)

\(h^{2}=133\).

Step4: Find \(h\)

\(h=\sqrt{133}\approx11.5\) (using a calculator to find the square - root of \(133\)).

Answer:

11.5 feet