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

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

Back

If each leg is 'x', then the hypotenuse is 'x√2'.

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides in 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'.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

Hypotenuse = 10√2.

Tags

CCSS.8.G.B.8

Front

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

Back

Longer leg = 5√3.

Tags

CCSS.HSG.CO.C.10

Front

What is the area of a 30°-60°-90° triangle with a shorter leg of 4?

Back

Area = (1/2) * base * height = (1/2) * 4 * (4√3) = 8√3.

Tags

CCSS.6.G.A.1

Front

What is the perimeter of a 45°-45°-90° triangle with legs of length 6?

Back

Perimeter = 6 + 6 + 6√2 = 12 + 6√2.

Tags

CCSS.8.G.B.8

Front

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

Back

Shorter leg = 12/2 = 6.

Tags

CCSS.8.G.B.8

Front

What is the sine of 30°?

Back

Sine of 30° = 1/2.

Tags

CCSS.HSG.SRT.C.7