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.

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'.

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'.

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).

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.

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).

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.

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.

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.

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.