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.

Tags

CCSS.8.G.B.8

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 shorter leg.

Tags

CCSS.HSG.CO.C.10

Front

Find x in a 45°-45°-90° triangle if one leg is 6.

Back

x = 6√2 (hypotenuse).

Tags

CCSS.8.G.B.8

Front

Find x in a 30°-60°-90° triangle if the shorter leg is 5.

Back

x = 5√3 (longer leg), x = 10 (hypotenuse).

Tags

CCSS.8.G.B.8

Front

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

Back

The lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Tags

CCSS.8.G.B.8

Front

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

Back

The length of the shorter leg is half the hypotenuse, and the longer leg is √3 times the shorter leg.

Tags

CCSS.HSG.CO.C.10

Front

If the hypotenuse of a 45°-45°-90° triangle is 10, what is the length of each leg?

Back

Each leg = 10/√2 = 5√2.

Tags

CCSS.8.G.B.8

Front

If the longer leg of a 30°-60°-90° triangle is 6√3, what is the length of the shorter leg?

Back

Shorter leg = 6.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the hypotenuse in a 30°-60°-90° triangle?

Back

Hypotenuse = 2 * (shorter leg).

Tags

CCSS.8.G.B.8

Front

What is the formula to find the longer leg in a 30°-60°-90° triangle?

Back

Longer leg = √3 * (shorter leg).

Tags

CCSS.8.G.B.8