Special Triangles

Front

What is a special triangle?

Back

A special triangle is a triangle with specific properties that make calculations easier, such as the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side lengths 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 a leg.

Front

What are the side lengths 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 opposite the 60° angle, and 2 is the hypotenuse.

Front

How do you find the hypotenuse in a 45-45-90 triangle?

Back

To find the hypotenuse, multiply the length of one leg by √2.

Front

How do you find the length of the longer leg in a 30-60-90 triangle?

Back

To find the longer leg, multiply the length of the shorter leg (opposite the 30° angle) by √3.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by the formula: Area = 1/2 * base * height.

Front

What is the Pythagorean theorem?

Back

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

Front

How can you use the Pythagorean theorem with special triangles?

Back

You can use the Pythagorean theorem to verify the side lengths of special triangles, ensuring they follow the established ratios.

Front

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

Back

The 30-60-90 triangle is often used in construction and design, where specific angles and lengths are required.

Front

What is the significance of the 45-45-90 triangle in real-life applications?

Back

The 45-45-90 triangle is commonly used in architecture and engineering, particularly in creating right angles.