Special Right Triangles and Geometric Mean

Front

What is a special right triangle?

Back

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

Front

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

Back

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

Front

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

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1 : 1 : √2, where the legs are equal and the hypotenuse is √2 times the length of each leg.

Front

How do you find the height of an equilateral triangle?

Back

The height (h) of an equilateral triangle can be found using the formula h = (√3/2) * a, where a is the length of a side.

Front

What is the geometric mean of two numbers?

Back

The geometric mean of two numbers a and b is the square root of their product, calculated as √(a*b).

Front

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

Back

The geometric mean of 2 and 25 is √(2*25) = √50 = 5√2.

Front

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

Back

The height (longer leg) is 7√3, since the longer leg is √3 times the shorter leg.

Front

What is the formula for the area of a triangle?

Back

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

Front

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

Back

Each leg of the triangle is 10, since the legs are equal and each leg is hypotenuse/√2.

Front

What is the relationship between the sides of a right triangle and the Pythagorean theorem?

Back

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