Question

two gymnasts are performing a floor routine before an audience. debbie and ramona both begin at the starting position. their locations at the end of their performance are shown on the diagram. debbie is 32.4 feet from the starting position and ramona is 40.5 feet away from debbie. at the end of their performance, how many feet is ramona from the starting position? diagram of a right triangle with starting position, debbie, and ramona as vertices options: a. 64.8 feet, b. 24.3 feet, c. 51.0 feet, d. 72.9 feet

Explanation:

Step1: Identify right triangle sides

Let starting position = \( S \), Debbie = \( D \), Ramona = \( R \). \( \triangle SRD \) is right-angled at \( S \). \( SD = 32.4 \), \( DR = 40.5 \).

Step2: Apply Pythagorean theorem

\( SR^2 + SD^2 = DR^2 \) → \( SR^2 = DR^2 - SD^2 \)

Step3: Calculate \( SR^2 \)

\( SR^2 = 40.5^2 - 32.4^2 = (40.5 - 32.4)(40.5 + 32.4) = 8.1×72.9 = 590.49 \)

Step4: Find \( SR \)

\( SR = \sqrt{590.49} = 24.3 \)

Answer:

B. 24.3 feet