30-60-90 Special Right Triangles

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side ratios are 1 : √3 : 2. The side opposite the 30° angle is 1, the side opposite the 60° angle is √3, and the hypotenuse is 2.

Front

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

Back

To find the hypotenuse, multiply the length of the shorter leg (opposite the 30° angle) by 2.

Front

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

Back

To find the longer leg (opposite the 60° angle), multiply the length of the shorter leg by √3.

Front

What is the relationship between the angles in a 30-60-90 triangle?

Back

A 30-60-90 triangle has angles measuring 30°, 60°, and 90°.

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The length of the shorter leg is 6 (12 divided by 2).

Front

If the shorter leg of a 30-60-90 triangle is 8, what is the length of the longer leg?

Back

The length of the longer leg is 8√3, which is approximately 13.86.

Front

What is the formula to calculate the area of a triangle?

Back

The area of a triangle is calculated using the formula: Area = 1/2 * base * height.

Front

In a 30-60-90 triangle, if the longer leg is 10√3, what is the length of the hypotenuse?

Back

The hypotenuse is 20 (10√3 divided by √3).

Front

What is the significance of the 30-60-90 triangle in real-world applications?

Back

30-60-90 triangles are often used in construction, architecture, and various fields of engineering due to their predictable ratios.

Front

How can you use the Pythagorean theorem in a 30-60-90 triangle?

Back

The Pythagorean theorem states that a² + b² = c², where c is the hypotenuse. You can use this to verify the side lengths of a 30-60-90 triangle.