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 x if the legs of a 45°-45°-90° triangle are 4. What is the length of the hypotenuse?

Back

x = 4√2

Front

Find y if the hypotenuse of a 30°-60°-90° triangle is 10. What is the length of the side opposite the 30° angle?

Back

y = 5

Front

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

Back

In a 45°-45°-90° triangle, the angles are 45°, 45°, and 90°. In a 30°-60°-90° triangle, the angles are 30°, 60°, and 90°.

Front

If the hypotenuse of a 30°-60°-90° triangle is 8, what is the length of the side opposite the 60° angle?

Back

4√3

Front

What is the formula for finding the length of the hypotenuse in a 45°-45°-90° triangle?

Back

Hypotenuse = leg × √2

Front

If one leg of a 45°-45°-90° triangle is 6, what is the length of the other leg?

Back

6 (both legs are equal in length).

Front

In a 30°-60°-90° triangle, if the side opposite the 30° angle is 4, what is the length of the hypotenuse?

Back

8 (hypotenuse = 2 × side opposite 30°).

Front

What is the value of x in a 45°-45°-90° triangle if the hypotenuse is 10?

Back

x = 5√2