Question

find the length of the missing side of the right triangle. round to three decimal places, if necessary. the legs of the right triangle are represented by a and b, and the hypotenuse is represented by c. a = 5, c = 13 a ( b = 14 ) b ( b = 9 ) c ( b = 13 ) d ( b = 12 )

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. We need to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values of \(a\) and \(c\)

Given \(a = 5\) and \(c=13\), then \(b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}\).

Step3: Calculate the square root

\(\sqrt{144}=12\).

Answer:

D. \(b = 12\)