Simplifying Radicals and Triangle Properties

Front

What is a 30-60-90 triangle?

Back

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

Front

How do you find the length of 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 relationship between the sides of a 45°-45°-90° triangle?

Back

The sides are in the ratio 1:1:√2.

Front

How do you simplify the radical √24?

Back

√24 can be simplified to 2√6.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

What is the Pythagorean theorem?

Back

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

Front

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

Back

The hypotenuse is 8.

Front

What is the length of the long leg in a 30-60-90 triangle if the short leg is 5?

Back

The long leg is 5√3.

Front

How do you find the length of the legs in a 45°-45°-90° triangle if the hypotenuse is 10?

Back

Each leg is 10/√2 or 5√2.

Front

What is the value of √(a²) for any real number a?

Back

|a| (the absolute value of a).