30-60-90 Triangles Exit Ticket

Front

What is a 30-60-90 triangle?

Back

A 30-60-90 triangle is 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

To find the hypotenuse, double the length of the shortest side. If the shortest side is 'x', then the hypotenuse is '2x'.

Tags

CCSS.8.G.B.8

Front

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

Back

The hypotenuse is 12, since it is double the shortest side (2 * 6 = 12).

Tags

CCSS.HSG.CO.C.10

Front

What is the formula to find the length of the side opposite the 60° angle in a 30-60-90 triangle?

Back

The length of the side opposite the 60° angle is given by 'x√3', where 'x' is the length of the shortest side.

Tags

CCSS.HSG.SRT.C.8

Front

If the hypotenuse of a 30-60-90 triangle is 20, what is the length of the shortest side?

Back

The shortest side is 10, since it is half the length of the hypotenuse (20 / 2 = 10).

Tags

CCSS.HSG.CO.C.10

Front

What is the value of the side opposite the 60° angle if the shortest side is 8?

Back

The side opposite the 60° angle is 8√3.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Front

How do you calculate the area of a 30-60-90 triangle?

Back

The area can be calculated using the formula: Area = (1/2) * base * height. For a 30-60-90 triangle, base = shortest side and height = side opposite the 60° angle.

Tags

CCSS.6.G.A.1

Front

If the shortest side of a 30-60-90 triangle is 5, what is the area?

Back

The area is 12.5, calculated as (1/2) * 5 * (5√3) = 12.5√3.

Tags

CCSS.6.G.A.1

Front

What is the sine of 30° in a 30-60-90 triangle?

Back

The sine of 30° is 1/2, which is the ratio of the length of the side opposite the 30° angle to the hypotenuse.

Tags

CCSS.HSG.SRT.C.6