Algebra-2

In a 30-60-90 right triangle, the ratio of the sides is determined by the angles of the triangle. The sides are in the ratio 1:√3:2, where the shorter leg is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is opposite the 90-degree angle.

Given that the longer leg of the triangle is 9, we can determine the value of the shorter leg.

Let's denote the length of the shorter leg as 'x'.

According to the ratio of the sides in a 30-60-90 triangle, we have:

x : 9 : 2x

To find the value of x, we can set up the equation:

x = 9/√3

Rationalizing the denominator by multiplying both numerator and denominator by √3:

x = (9/√3) * (√3/√3)
x = (9√3)/3
x = 3√3

Therefore, the value of the shorter leg is 3√3.

Hence, the correct answer is B.

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