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 sides opposite the 45° angles are equal, 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 side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the length of the side opposite the 30° angle.

Front

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

Back

If each leg is 'x', then the hypotenuse is 'x√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 7.

Back

7√2

Front

Find the length of the longer leg in a 30-60-90 triangle if the shorter leg is 3.

Back

3√3

Front

What is the measure of the angles in a 45-45-90 triangle?

Back

45°, 45°, and 90°.

Front

What is the measure of the angles in a 30-60-90 triangle?

Back

30°, 60°, and 90°.

Front

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

Back

6.

Front

If the legs of a 45-45-90 triangle are each 4, what is the length of the hypotenuse?

Back

4√2.