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.

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

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

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'.

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.

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.

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.

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.

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.

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.