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, such as the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side length ratios in 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 a leg.

Front

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

Back

Multiply the length of a leg by √2.

Front

If one leg of a 45-45-90 triangle is 5, what is the length of the hypotenuse?

Back

5√2.

Front

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

Back

The lengths of the legs are equal.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

What are the side length ratios in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

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 (opposite the 30° angle) by √3.

Front

If the shorter leg of a 30-60-90 triangle is 4, what is the length of the longer leg?

Back

4√3.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 3?

Back

6.