Special Right Triangles and Geometric Mean

What is the significance of the geometric mean in real-world applications?

• It is used to average ratios, percentages, and other multiplicative factors in finance and statistics.

• It is primarily used to calculate the average of a set of numbers in basic arithmetic.

• It is used to determine the median of a data set in statistical analysis.

• It is mainly applied in geometry to find the area of shapes.

If the hypotenuse of a 45-45-90 triangle is 10√2, what is the length of each leg?

• 5

• 10

• 15

• 20

What is a special right triangle?

• A triangle with all angles equal to 60 degrees.

• A right triangle with specific angle measures and side length ratios, such as the 30-60-90 triangle and the 45-45-90 triangle.

• Any triangle that has one angle measuring 90 degrees.

• A triangle that can be inscribed in a circle.

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

• 1 : 1 : 1

• 1 : √2 : 2

• 1 : √3 : 2

• 1 : 2 : √3

What is the measure of the angles in a 45-45-90 triangle?

• 30 degrees, 60 degrees, 90 degrees

• 45 degrees, 45 degrees, 90 degrees

• 60 degrees, 60 degrees, 60 degrees

• 90 degrees, 45 degrees, 45 degrees

What is the height of a 30-60-90 triangle if the shorter leg is 7?

• 7

• 14

• 7√3

• 10

What is the formula for the area of a triangle?

• A = base * height

• A = (1/2) * base * height

• A = base + height

• A = (1/3) * base * height

How do you calculate the geometric mean of 2 and 25?

• √(2*25) = √50 = 5√2

• (2 + 25) / 2 = 13.5

• (2 * 25) / 2 = 25

• √(2 + 25) = √27

How do you find the height of a triangle using the Pythagorean theorem?

• By using the Pythagorean theorem to solve for the height when you know the lengths of the base and the hypotenuse.

• By calculating the area of the triangle and dividing it by the base length.

• By measuring the angle opposite to the height and using trigonometric ratios.

• By adding the lengths of all three sides of the triangle.

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

• 1 : 1 : 1

• 1 : 1 : √3

• 1 : 1 : √2

• 1 : 2 : √2