Answer:
Special right triangles are triangles that have angles that measure 30 degrees, 60 degrees, and 90 degrees or angles that measure 45 degrees, 45 degrees, and 90 degrees. Here are the steps to find the missing sides of these triangles:
For a 30-60-90 triangle:
- Identify the longest side. This side is opposite the 90-degree angle and is called the hypotenuse.
- The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.
- The side opposite the 30-degree angle is half the length of the hypotenuse.
For example, if the hypotenuse of a 30-60-90 triangle measures 10 cm, then the side opposite the 60-degree angle would be √3 x 5 cm = 8.66 cm, and the side opposite the 30-degree angle would be 5 cm.
For a 45-45-90 triangle:
- Identify the longest side. This side is opposite the 90-degree angle and is called the hypotenuse.
- The side opposite each of the 45-degree angles is equal in length.
- Each side opposite a 45-degree angle is √2 times the length of the adjacent side.
For example, if the hypotenuse of a 45-45-90 triangle measures 10 cm, then each of the other two sides would be 10/√2 cm ≈ 7.07 cm.
These formulas can be used to find the missing sides of special right triangles if you know the length of one side or the length of the hypotenuse.