30-60-90 Triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1 : √3 : 2.

Tags

CCSS.8.G.B.8

Front

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

Back

The ratio of the sides is 1 : √3 : 2, corresponding to the angles 30°, 60°, and 90° respectively.

Tags

CCSS.HSG.CO.C.10

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 4?

Back

The hypotenuse is 8, since it is twice the length of the shorter leg.

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

The shorter leg is 6, since the longer leg is √3 times the shorter leg.

Tags

CCSS.HSG.CO.C.10

Front

How do you find the length of the longer leg in a 30-60-90 triangle?

Back

Multiply the length of the shorter leg by √3.

Tags

CCSS.8.G.B.8

Front

How do you find the length of the shorter leg in a 30-60-90 triangle?

Back

Divide the length of the longer leg by √3.

Tags

CCSS.8.G.B.8

Front

What is the length of the longer leg if the hypotenuse is 10?

Back

The longer leg is 5√3, since it is half the hypotenuse multiplied by √3.

Tags

CCSS.HSG.CO.C.10

Front

In a 30-60-90 triangle, if the shorter leg is x, what is the length of the hypotenuse?

Back

The hypotenuse is 2x.

Tags

CCSS.8.G.B.8

Front

In a 30-60-90 triangle, if the longer leg is y, what is the length of the shorter leg?

Back

The shorter leg is y/√3.

Tags

CCSS.8.G.B.8

Front

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

Back

The area is 8, calculated as (1/2) * base * height = (1/2) * 4 * 4√3.

Tags

CCSS.6.G.A.1