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, commonly the 45-45-90 triangle and the 30-60-90 triangle.

Front

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

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30° angle, √3 is opposite the 60° angle, and 2 is the hypotenuse.

Front

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

Back

Multiply the length of one leg by √2 to find the hypotenuse.

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 to find the longer leg (opposite the 60° angle).

Front

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

Back

The hypotenuse is 5√2.

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The shorter leg is 6.

Front

What is the formula for the area of a triangle?

Back

The area A of a triangle is given by A = ½ * base * height.

Front

If the base of a triangle is 10 and the height is 5, what is the area?

Back

The area is 25.

Front

In a 30-60-90 triangle, if the longer leg is 8√3, what is the length of the hypotenuse?

Back

The hypotenuse is 16.