Final answer:
To solve a special right triangle, you need to use the relationships between the side lengths and angles. For a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. For a 45-45-90 triangle, the side lengths are in the ratio 1:1:√2. Multiply these ratios by a common factor to find the side lengths in simplified, rational numbers.
Step-by-step explanation:
A special right triangle is a right triangle that has angles of specific measures (30 degrees, 45 degrees, or 60 degrees) and side lengths that are in a certain ratio. To solve a special right triangle, you need to use the relationships between the side lengths and angles. For example, in a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. To find the side lengths in simplified, rational numbers, you can multiply the ratio by a common factor.
For a 45-45-90 triangle, the side lengths are in the ratio 1:1:√2. Again, you can multiply the ratio by a common factor to find the side lengths in simplified, rational numbers.
In summary, to solve a special right triangle, you need to know the angle measures and the side lengths ratios. From there, you can use the relationships between the angles and side lengths to find the values of the sides in simplified, rational numbers.