Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios that make calculations easier. The two main types are 45-45-90 and 30-60-90 triangles.

Front

What are the angle measures of a 45-45-90 triangle?

Back

The angle measures are 45°, 45°, and 90°.

Front

What is the side length ratio of a 45-45-90 triangle?

Back

The side lengths are in the ratio 1:1:√2, where the legs are equal and the hypotenuse is √2 times the length of each leg.

Front

What are the angle measures of a 30-60-90 triangle?

Back

The angle measures are 30°, 60°, and 90°.

Front

What is the side length ratio of a 30-60-90 triangle?

Back

The side lengths are in the ratio 1:√3:2, where the shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is the longest side.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle?

Back

Front

How do you find the length of the longer leg in a 30-60-90 triangle?

Back

Front

What is the formula to find the area of a right triangle?

Back

Front

In a 45-45-90 triangle, if the legs are each 6 units long, what is the length of the hypotenuse?

Back