To find the missing side lengths and angle measures of special right triangles, we'll discuss two types: the 45-45-90 triangle and the 30-60-90 triangle.
1. 45-45-90 Triangle:
In a 45-45-90 triangle, the two legs are congruent, and the hypotenuse is √2 times the length of each leg.
Side Lengths:
Let's assume the length of one leg is "a." Then, the length of the other leg is also "a," and the length of the hypotenuse is √2 times "a."
Angle Measures:
Each acute angle in a 45-45-90 triangle is 45 degrees, and the right angle is 90 degrees.
2. 30-60-90 Triangle:
In a 30-60-90 triangle, the lengths of the sides have specific ratios. The ratio is as follows:
Side Lengths:
- The length of the shorter leg (opposite the 30-degree angle) is "a."
- The length of the longer leg (opposite the 60-degree angle) is "a√3."
- The length of the hypotenuse (opposite the 90-degree angle) is 2a.
Angle Measures:
- The acute angles in a 30-60-90 triangle are 30 degrees and 60 degrees, while the right angle is 90 degrees.
By using these ratios and angle measures, you can find the missing side lengths and angle measures of each triangle. Just ensure you have enough information or known side lengths/angle measures to apply the ratios correctly.