Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for simplified calculations of side lengths. The two main types are the 45°-45°-90° triangle and the 30°-60°-90° triangle.

Front

What are the side ratios of a 45°-45°-90° triangle?

Back

In a 45°-45°-90° triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

What are the side ratios of a 30°-60°-90° triangle?

Back

In a 30°-60°-90° triangle, the length of the side opposite the 30° angle is half the length of the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

If the leg of a 45°-45°-90° triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

If the shorter leg of a 30°-60°-90° triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 10.

Front

What is the length of the longer leg in a 30°-60°-90° triangle if the shorter leg is 5?

Back

The longer leg is 5√3.

Front

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

Back

Multiply the length of one leg by √2.

Front

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

Back

Multiply the length of the shorter leg by √3.

Front

What is the relationship between the angles in a 45°-45°-90° triangle?

Back

Both angles are 45°, making it an isosceles right triangle.

Front

What type of triangle is formed by angles 30°, 60°, and 90°?

Back

A 30°-60°-90° triangle.