Question

which triangle is a 30°-60°-90° triangle? 10 5 5√3 15 5 5√3 10 5 10√3 15 10 5√3

Explanation:

Step1: Recall 30-60-90 side ratios

A 30°-60°-90° triangle has side lengths in the ratio $1 : \sqrt{3} : 2$, where the shortest side (opposite 30°) is $x$, the longer leg (opposite 60°) is $x\sqrt{3}$, and the hypotenuse (opposite 90°) is $2x$.

Step2: Test first triangle sides

Sides: $5$, $5\sqrt{3}$, $10$.
Check ratio: $5 : 5\sqrt{3} : 10 = 1 : \sqrt{3} : 2$ (divide all by 5). This matches the 30-60-90 ratio.

Step3: Verify other options (optional)

• Second triangle: $5$, $5\sqrt{3}$, $15$. Ratio: $1 : \sqrt{3} : 3$ (does not match).
• Third triangle: $5$, $10\sqrt{3}$, $10$. Ratio: $1 : 2\sqrt{3} : 2$ (does not match).
• Fourth triangle: $10$, $5\sqrt{3}$, $15$. Ratio: $2 : \sqrt{3} : 3$ (does not match).

Answer:

The triangle with side lengths 5, $5\sqrt{3}$, and 10 (the first option) is a 30°-60°-90° triangle.