In a 30-60-90 triangle, the sides are in a specific ratio. The lengths of the sides opposite the 30°, 60°, and 90° angles are in the ratio of 1 : √3 : 2.
Given that the hypotenuse (the side opposite the 90° angle) is 30, we can use the ratio to find the lengths of the other sides.
The longer leg is opposite the 60° angle in this triangle, and according to the ratio, it is equal to the hypotenuse multiplied by √3/2:
Length of the longer leg = hypotenuse × (√3 / 2) = 30 × (√3 / 2) = 15√3.
To get a numerical approximation, √3 is approximately 1.732, so:
15√3 ≈ 15 × 1.732 ≈ 25.98.
Therefore, the length of the longer leg is 15√3, or approximately 25.98.