In a 30-60-90 triangle, the sides are in a specific ratio that helps us easily determine the lengths of the sides based on the shortest leg. The ratio of the sides in a 30-60-90 triangle is 1 : √3 : 2. This means:
- The shortest leg (opposite the 30-degree angle) is 1 part.
- The longer leg (opposite the 60-degree angle) is √3 parts.
- The hypotenuse (opposite the right angle) is 2 parts.
Given that the shorter leg is 8 m, we can set up the following equation:
If the shorter leg corresponds to 1 part in the ratio, we have:
- Shorter leg = 1 part = 8 m
To find the length of the hypotenuse (which corresponds to 2 parts), we can use the ratio:
- Hypotenuse = 2 parts = 2 x (Length of shorter leg) = 2 x 8 m = 16 m
Thus, the length of the hypotenuse in this 30-60-90 triangle, when the shorter leg is 8 m, is 16 meters.