Special Right Triangles

Front

What are the properties of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are of equal length, and the length of the hypotenuse is equal to the length of a leg multiplied by √2.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

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

Front

How do you find the hypotenuse in a 45-45-90 triangle if one leg is known?

Back

Multiply the length of the leg by √2 to find the hypotenuse.

Front

How do you find the length of a leg in a 30-60-90 triangle if the hypotenuse is known?

Back

Divide the length of the hypotenuse by 2 to find the length of the leg opposite the 30-degree angle, and multiply that length by √3 to find the length of the leg opposite the 60-degree angle.

Front

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

Back

The area of a right 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 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 value of the hypotenuse in a 30-60-90 triangle if the shorter leg is 5?

Back

The hypotenuse would be 10, as it is twice the length of the shorter leg.

Front

What is the value of the longer leg in a 30-60-90 triangle if the shorter leg is 5?

Back

The longer leg would be 5√3, as it is √3 times the length of the shorter leg.

Front

How do you calculate the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

Back

Divide the length of the hypotenuse by √2 to find the length of each leg.

Front

What is the significance of special right triangles in geometry?

Back

Special right triangles provide specific ratios that simplify calculations in trigonometry and geometry, making it easier to solve problems involving right triangles.