Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios that make calculations easier. The two main types are 45°-45°-90° and 30°-60°-90° triangles.

Front

What are the side length ratios of a 45°-45°-90° triangle?

Back

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

Front

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

Back

In a 30°-60°-90° triangle, the length of the side opposite the 30° angle is half the length of the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

How do you determine if a set of numbers can form a right triangle?

Back

To determine if a set of numbers can form a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers (Pythagorean theorem).

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What is the square root of a number?

Back

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4.

Front

If one leg of a 45°-45°-90° triangle is 6, what is the length of the hypotenuse?

Back

The hypotenuse is 6√2.

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 (opposite the 30° angle) is 6.

Front

What is the relationship between the angles in a right triangle?

Back

In a right triangle, one angle is always 90°, and the sum of the other two angles is always 90°.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) × base × height.