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 formula for finding the hypotenuse of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg.

Front

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

Back

To find the length of a leg in a 45-45-90 triangle, divide the length of the hypotenuse by √2.

Front

What is the relationship between the sides 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 shorter leg, √3 is the length of the longer leg, and 2 is the length of the hypotenuse.

Front

If the hypotenuse of a 45-45-90 triangle is 8√2, what is the length of each leg?

Back

Each leg would be 8, since the leg length is the hypotenuse divided by √2.

Front

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

Back

The longer leg would be 5√3, and the hypotenuse would be 10.

Front

How do you calculate the area of a right triangle?

Back

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

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.

Front

What is the formula for the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse and a and b are the legs.

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean theorem: c = √(a² + b²).