Special Right Triangles A

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 the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side 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

If one leg of a 45-45-90 triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√2.

Front

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

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30° angle, √3 is the length of the side opposite the 60° angle, and 2 is the length of the hypotenuse.

Front

If the shorter leg of a 30-60-90 triangle is 4, what are the lengths of the other sides?

Back

The longer leg is 4√3, and the hypotenuse is 8.

Front

What is the formula for finding the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) × base × height.

Front

How do you find the height of a right triangle if you know the lengths of the legs?

Back

In a right triangle, one leg can be considered the base, and the other leg can be considered the height.

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

How can the Pythagorean theorem be applied to special right triangles?

Back

In special right triangles, the Pythagorean theorem can be used to verify the side length ratios, such as confirming that (√2)² = 1 + 1 for a 45-45-90 triangle.

Front

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

Back

The 30-60-90 triangle is often used in construction and design, as it helps in creating angles and dimensions that are easy to work with.