Special right triangles are a unique type of triangle that have angles and side lengths that follow specific patterns. These triangles are important to understand in geometry, as they can help solve problems involving angles and sides of triangles. One of the most common special right triangles is the 45-45-90 triangle, where the two acute angles are both 45 degrees and the hypotenuse is √2 times the length of the legs.
Another special right triangle is the 30-60-90 triangle, where one angle is 30 degrees, another is 60 degrees, and the hypotenuse is twice the length of the shorter leg. These special triangles have unique properties that make them useful in a variety of geometric problems.
Special Right Triangles Worksheet
Below is a worksheet that includes problems involving special right triangles. Use the properties of these triangles to solve each problem and find the missing side lengths or angles. Make sure to apply the rules of special right triangles correctly to determine the correct answers.
1. In a 45-45-90 triangle, if one leg has a length of 5 cm, what is the length of the hypotenuse?
2. In a 30-60-90 triangle, if the shorter leg has a length of 6 units, what is the length of the longer leg?
3. Given a 30-60-90 triangle with a hypotenuse of 10 inches, what are the lengths of the other two sides?
4. If the shorter leg of a 45-45-90 triangle is 8 meters, what is the length of the other leg?
5. In a 30-60-90 triangle, if the longer leg is 12 cm, what is the length of the shorter leg?
After completing the worksheet, check your answers to ensure that you have applied the properties of special right triangles correctly. Practice more problems involving special right triangles to strengthen your understanding of these unique triangles and their properties.