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 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

Find the length of the hypotenuse in a 45°-45°-90° triangle with legs of length 10.

Back

10√2

Front

Find the length of the side opposite the 30° angle in a 30°-60°-90° triangle with a hypotenuse of 20.

Back

10

Front

What is the ratio of the sides in a 30°-60°-90° triangle?

Back

1 : √3 : 2 (opposite 30° : opposite 60° : hypotenuse)

Front

If one leg of a 45°-45°-90° triangle is 5, what is the length of the hypotenuse?

Back

5√2

Front

What is the area of a 30°-60°-90° triangle with a base of 10 and height of 10√3?

Back

50

Front

Find the length of the side opposite the 60° angle in a 30°-60°-90° triangle with a side opposite the 30° angle measuring 5.

Back

5√3

Front

What is the relationship between the angles in a right triangle?

Back

The sum of the angles in a right triangle is always 180°, with one angle being 90°.

Front

If the hypotenuse of a 45°-45°-90° triangle is 14.14, what is the length of each leg?

Back

10