Question

30/60/90 triangle, long leg is 6, solve for short leg

Answer 1

The length of the short leg in a 30/60/90 triangle with a long leg of 6 is 2√3.

Step-by-step explanation:

To solve for the short leg of a 30/60/90 triangle where the long leg is 6, we use the properties of this special right triangle. In a 30/60/90 triangle, the length of the shorter leg, which we'll call a, is half the length of the hypotenuse, and the length of the longer leg, which we'll call b, is the length of the shorter leg times √3. Since we know that b is 6, we can use the relationship a = b / √3 to solve for a.

Here's the calculation:

1. Write down the known ratio: a = b / √3.
2. Substitute the given value for the longer leg (b = 6): a = 6 / √3.
3. Simplify the expression to find the short leg a: a = 6√3 / 3 = 2√3.

Therefore, the length of the short leg of the triangle is 2√3.