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 most common 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 is the length of the hypotenuse in a 30-60-90 triangle if the short leg is 6?

Back

The hypotenuse is 12, calculated as 2 times the short leg (2 * 6 = 12).

Front

If the hypotenuse of a 30-60-90 triangle is 14, what is the length of the short leg?

Back

The short leg is 7, calculated as half of the hypotenuse (14 / 2 = 7).

Front

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

Back

The longer leg is 3√3, calculated as the short leg multiplied by √3 (3 * √3).

Front

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

Back

In a 45-45-90 triangle, both angles are 45°, making it an isosceles right triangle where the legs are equal in length.

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

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

Back

The hypotenuse is 4√2, calculated as the leg length multiplied by √2 (4 * √2).

Front

What is the formula to find the length of the longer leg in a 30-60-90 triangle?

Back

The longer leg can be found using the formula: Longer leg = Short leg * √3.

Front

In a 30-60-90 triangle, if the longer leg is 6√3, what is the length of the short leg?

Back

The short leg is 6, calculated by dividing the longer leg by √3 (6√3 / √3 = 6).