Question

find the unknown length in the right triangle. the unknown length is approximately (type a whole number or decimal rounded to the nearest thousandth as needed.)

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse, and \( a, b \) are the legs. Let \( a = 11 \), \( c = 13 \), find \( b \). So \( b^2 = c^2 - a^2 \).
\( b^2 = 13^2 - 11^2 = 169 - 121 = 48 \)

Step2: Solve for \( b \)

Take square root of 48: \( b = \sqrt{48} \approx 6.928 \)

Answer:

\( 6.928 \)