Question

what is the length of the short leg of a 30 - 60 - 90? * 1 point x x√2 x√3 2x

Explanation:

Step1: Recall the side - length ratios of a 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the hypotenuse is \(c\), the short leg (opposite the 30° angle) is \(a\), and the long leg (opposite the 60° angle) is \(b\), the ratio of the sides is \(a:b:c = 1:\sqrt{3}:2\). Let the short leg be \(x\), the long leg be \(x\sqrt{3}\), and the hypotenuse be \(2x\).

Step2: Analyze the given options

• The option \(x\sqrt{2}\) is the ratio for the non - hypotenuse sides of a 45 - 45 - 90 triangle (isosceles right - triangle) where the ratio of sides is \(1:1:\sqrt{2}\).
• The option \(x\sqrt{3}\) is the length of the long leg in a 30 - 60 - 90 triangle.
• The option \(2x\) is the length of the hypotenuse in a 30 - 60 - 90 triangle.

Answer:

\(x\)