Special Right Triangles Review Solutions and Explanations

For solving problems involving 45-45-90 and 30-60-90 figures, start by recalling the key properties of these shapes. In a 45-45-90 figure, the legs are equal, and the hypotenuse is √2 times the length of a leg. For a 30-60-90 shape, the ratio between the sides is 1:√3:2, with the shortest side opposite the 30-degree angle.

Use these relationships to find missing sides: In problems where one side is known, apply these ratios to determine the other sides. For example, if the hypotenuse of a 30-60-90 figure is known, you can immediately calculate the other two sides using the ratio 1:√3:2.

By following these principles, you can quickly solve most problems involving these geometric figures. Check your results against this guide to verify your calculations and ensure accuracy.