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 easy calculation of side lengths. The two main types are the 30-60-90 triangle and the 45-45-90 triangle.

Front

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

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2. The shortest side (opposite the 30° angle) is 'x', the longer leg (opposite the 60° angle) is 'x√3', and the hypotenuse is '2x'.

Front

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

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1 : 1 : √2. Both legs are equal, and the hypotenuse is '√2' times the length of each leg.

Front

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

Back

To find the hypotenuse in a 30-60-90 triangle, multiply the length of the shorter leg (opposite the 30° angle) by 2.

Front

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

Back

To find the length of the longer leg (opposite the 60° angle) in a 30-60-90 triangle, multiply the length of the shorter leg by √3.

Front

If the shorter leg of a 30-60-90 triangle is 7, what is the length of the hypotenuse?

Back

The hypotenuse is 14, since it is double the length of the shorter leg (7 * 2 = 14).

Front

If the shorter leg of a 30-60-90 triangle is 7, what is the length of the longer leg?

Back

The longer leg is 7√3, since it is the shorter leg multiplied by √3.

Front

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

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Front

In a 45-45-90 triangle, if one leg is 10, what is the length of the hypotenuse?

Back

The hypotenuse is 10√2, since it is the length of a leg multiplied by √2.

Front

In a 30-60-90 triangle, if the hypotenuse is 20, what is the length of the shorter leg?

Back

The shorter leg is 10, since it is half the length of the hypotenuse (20 / 2 = 10).