Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The legs are of equal length, and the hypotenuse is √2 times the length of a leg.

Front

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

Back

If the length of each leg is 'a', then the hypotenuse is 'a√2'.

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30°, 60°, and 90°. The sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides in a 30-60-90 triangle?

Back

If the length of the short leg (opposite the 30° angle) is 'a', then the long leg (opposite the 60° angle) is 'a√3' and the hypotenuse is '2a'.

Front

How do you find the hypotenuse in a 30-60-90 triangle if given the short leg?

Back

Multiply the length of the short leg by 2.

Front

How do you find the long leg in a 30-60-90 triangle if given the short leg?

Back

Multiply the length of the short leg by √3.

Front

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

Back

4√2.

Front

In a 30-60-90 triangle, if the short leg is 5, what is the length of the hypotenuse?

Back

10.

Front

In a 30-60-90 triangle, if the short leg is 4, what is the length of the long leg?

Back

4√3.

Front

If the hypotenuse of a 45-45-90 triangle is 8√2, what is the length of each leg?

Back

8.