Question

find the length of the unknown side of the right triangle. in each case, a and b represent the lengths of the legs and c represents the length of the hypotenuse. a=9, b=12; find c. a. 63 b. 15 c. 162 d. 225

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem is \( c = \sqrt{a^2 + b^2} \), where \( a = 9 \) and \( b = 12 \).
First, calculate \( a^2 \) and \( b^2 \):
\( a^2 = 9^2 = 81 \)
\( b^2 = 12^2 = 144 \)

Step2: Sum the squares

Add \( a^2 \) and \( b^2 \):
\( a^2 + b^2 = 81 + 144 = 225 \)

Step3: Take the square root

Take the square root of the sum to find \( c \):
\( c = \sqrt{225} = 15 \)

Answer:

B. 15