Questions: The hypotenuse of a right triangle is 20 units long. One leg of the triangle is 12 units long as shown in the figure. What is the length of the other leg? a. 16.8 units b. 20 units c. 16 units d. 23 units

Solution Steps

The hypotenuse of the right triangle is 20 units, and one leg is 12 units.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two legs (a and b): \[ c^2 = a^2 + b^2 \]

Given \( c = 20 \) and \( a = 12 \): \[ 20^2 = 12^2 + b^2 \] \[ 400 = 144 + b^2 \]

\[ b^2 = 400 - 144 \] \[ b^2 = 256 \] \[ b = \sqrt{256} \] \[ b = 16 \]

Final Answer