9.2 special right triangles

Front

What is the ratio of the sides in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1:√3:2.

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle if you are given the long leg?

Back

To find the hypotenuse, divide the length of the long leg by √3 and then multiply by 2.

Front

What is the length of the legs in a 45-45-90 triangle if the hypotenuse is 8√2?

Back

In a 45-45-90 triangle, the legs are equal, and each leg is the hypotenuse divided by √2. Therefore, each leg is 8.

Front

What is the formula for the diagonal of a square in terms of its side length?

Back

The diagonal d of a square with side length s is given by the formula d = s√2.

Front

In a 30-60-90 triangle, if the short leg is n, what is the length of the long leg?

Back

The length of the long leg is n√3.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If the short leg of a 30-60-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 8, calculated as 4 multiplied by 2.

Front

How do you express the length of the long leg in a 30-60-90 triangle in terms of the short leg?

Back

The long leg is √3 times the length of the short leg.

Front

What is the length of the diagonal of a square with a side length of 95?

Back

The length of the diagonal is 95√2.

Front

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

Back

The short leg is 5, calculated as 10 divided by 2.