Questions: Exam number: 700193RR Exam Guidelines Exam Instructions Question 17 of 20 : Select the best answer for the question. 17. A right triangle has a hypotenuse c=12.6 and a leg b=8.5. What is the approximate length of leg a? A. 10.2 B. 8.4 C. 9.3 D. 15.2 Mark for review (Will be highlighted on the review page)

Solution Steps

To find the length of leg \( a \) in a right triangle when the hypotenuse \( c \) and one leg \( b \) are known, we can use the Pythagorean theorem. The theorem states that \( a^2 + b^2 = c^2 \). We can rearrange this to solve for \( a \) as \( a = \sqrt{c^2 - b^2} \).

Given a right triangle with hypotenuse \( c = 12.6 \) and one leg \( b = 8.5 \), we can use the Pythagorean theorem, which states: \[ a^2 + b^2 = c^2 \] We need to solve for \( a \).

Rearranging the equation to isolate \( a \): \[ a^2 = c^2 - b^2 \] Taking the square root of both sides gives: \[ a = \sqrt{c^2 - b^2} \]

Substituting the known values into the equation: \[ a = \sqrt{12.6^2 - 8.5^2} \]

Calculating the squares: \[ 12.6^2 = 158.76 \quad \text{and} \quad 8.5^2 = 72.25 \] Thus, \[ a = \sqrt{158.76 - 72.25} = \sqrt{86.51} \approx 9.3011 \]

Final Answer