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 opposite these angles are in the ratio 1 : √3 : 2.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

In a 30-60-90 triangle, if the shortest side (opposite the 30° angle) is 'x', then the side opposite the 60° angle is 'x√3', and the hypotenuse (opposite the 90° angle) is '2x'.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

If the length of the shorter leg (opposite the 30° angle) is 'a', then the hypotenuse is '2a'.

Tags

CCSS.8.G.B.8

Front

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

Back

If the length of the shorter leg (opposite the 30° angle) is 'a', then the longer leg (opposite the 60° angle) is 'a√3'.

Tags

CCSS.8.G.B.8

Front

If the shorter leg of a 30-60-90 triangle is 6, what is the length of the hypotenuse?

Back

The hypotenuse is 12.

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.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the area of a 30-60-90 triangle?

Back

Area = (1/2) * base * height. For a 30-60-90 triangle, Area = (1/2) * (shorter leg) * (longer leg) = (1/2) * x * (x√3) = (√3/2) * x².

Tags

CCSS.HSG.SRT.D.9

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the shorter leg?

Back

The shorter leg is 5.

Tags

CCSS.8.G.B.8

Front

What is the value of the longer leg if the hypotenuse is 10 in a 30-60-90 triangle?

Back

The longer leg is 5√3.

Tags

CCSS.8.G.B.8

Front

In a 30-60-90 triangle, if the longer leg is 12√3, what is the length of the hypotenuse?

Back

The hypotenuse is 24.

Tags

CCSS.8.G.B.8