Question

question 3 of 10 which set of values could be the side lengths of a 30 - 60 - 90 triangle? a. {5, 5\sqrt{3}, 10} b. {5, 10, 10\sqrt{2}} c. {5, 5\sqrt{2}, 10} d. {5, 10, 10\sqrt{3}}

Explanation:

Step1: Recall 30-60-90 ratio

Ratio: \( x : x\sqrt{3} : 2x \) (short leg: long leg: hypotenuse)

Step2: Check Option A

Short leg \( x=5 \), long leg \( 5\sqrt{3} \), hypotenuse \( 2x=10 \). Matches ratio.

Step3: Verify others

B, C have \( \sqrt{2} \) (45-45-90). D has wrong long leg.

Answer:

A. (5, 5√3, 10)