which triangle is a 30° - 60° - 90° triangle?\n10\n5\n5√3\n15\n5\n5√3\n10\n5\n10√3\n15\n10\n5√3

Explanation:

Step1: Recall side - ratio property

In a 30° - 60° - 90° triangle, if the shorter leg (opposite 30°) is $a$, the longer leg (opposite 60°) is $a\sqrt{3}$ and the hypotenuse is $2a$.

Step2: Check each option

For the first option: If $a = 5$, then $2a=10$ and $a\sqrt{3}=5\sqrt{3}$. The side - lengths satisfy the 30° - 60° - 90° triangle ratio. For the second option: If $a = 5$, then $2a = 10\neq15$. For the third option: If $a = 5$, then $a\sqrt{3}=5\sqrt{3}\neq10\sqrt{3}$. For the fourth option: If $a = 5\sqrt{3}$, then $2a = 10\sqrt{3}\neq15$.

Answer:

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