Simplifying Radicals and Triangle Properties

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles measure 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

Front

How do you find the long leg in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by √3.

Front

What is the relationship between the short leg and the hypotenuse in a 30-60-90 triangle?

Back

The hypotenuse is twice the length of the short leg.

Front

How do you find the short leg in a 30-60-90 triangle if the long leg is known?

Back

Divide the length of the long leg by √3.

Front

What is the formula to simplify √150?

Back

√150 = √(25 * 6) = 5√6.

Front

What is the hypotenuse of a 30-60-90 triangle if the short leg is 4?

Back

The hypotenuse is 8.

Front

What is the long leg of a 30-60-90 triangle if the short leg is 4?

Back

The long leg is 4√3.

Front

What is the value of √(a^2 + b^2) in a right triangle?

Back

It represents the length of the hypotenuse.

Front

How do you simplify √(x^2)?

Back

√(x^2) = |x|.

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse.