Special Right Triangles 45-45-90 and 30-60-90

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 each leg.

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30°, 60°, and 90°. The length of the side opposite the 30° angle is half the length of the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

If the legs are of length 'a', then the hypotenuse is 'a√2'.

Front

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

Back

If the shorter leg (opposite the 30° angle) is 'x', then the longer leg (opposite the 60° angle) is 'x√3' and the hypotenuse is '2x'.

Front

Find the length of the hypotenuse in a 45-45-90 triangle with legs of length 4.

Back

The hypotenuse is 4√2.

Front

Find the length of the longer leg in a 30-60-90 triangle if the shorter leg is 5.

Back

The longer leg is 5√3.

Front

What is the value of x in a 30-60-90 triangle if the hypotenuse is 12?

Back

The value of x (the shorter leg) is 6.

Front

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

Back

The longer leg is 3√3.

Front

If the legs of a 45-45-90 triangle are 7, what is the hypotenuse?

Back

The hypotenuse is 7√2.

Front

In a 30-60-90 triangle, if the hypotenuse is 10, what is the length of the shorter leg?

Back

The length of the shorter leg is 5.