Algebra-2

In a right triangle with a 30-degree angle, the hypotenuse is labeled as , and the longer leg is labeled as 'x'. We need to find the value of x.

 

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

 

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 x : x√3 : 2x, 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.

 

So, in this case, we have:

 

x : x√3 : 2x

 

According to the ratio of the sides in a 30-60-90 triangle, we can set up the equation:

 

2x =

 

To solve for x, we divide both sides of the equation by 2:

 

x =

 

Therefore, the value of the shorter leg is

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