To find the length of the side opposite the 60-degree angle in a triangle, we can use the properties of a 30-60-90 triangle, which offers a specific ratio for the lengths of its sides. In a 30-60-90 triangle, the sides are in the ratio:
- 1 : √3 : 2
Here, the side opposite the 30-degree angle is the shortest and has a length of 1x (let’s say this represents the shortest side), the side opposite the 60-degree angle has a length of √3x, and the side opposite the 90-degree angle (the hypotenuse) has a length of 2x.
If we know the length of the hypotenuse or the length of the side opposite the 30-degree angle, we can easily find the length of the side opposite the 60-degree angle using the ratios above. For instance, if the hypotenuse is known to be 10 units, the side opposite the 60-degree angle would be:
Side opposite 60° = √3/2 * Hypotenuse = √3/2 * 10 = 5√3 ≈ 8.66 units.
It is important to remember that if the triangle is not a 30-60-90 triangle, you might need to use the Law of Sines or cosine values based on the information provided in the triangle. If you provide the lengths of other sides or angles, we can use other trigonometric functions to determine the length as well.