24-25 Special Right 30-60-90 Assignment

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

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° angle is 'x', the side opposite the 60° angle is 'x√3', and the hypotenuse is '2x'.

Front

How do you find the height of an equilateral triangle?

Back

The height (h) can be found using the formula h = (√3/2) * side length.

Front

If the perimeter of an equilateral triangle is 90 inches, what is the length of one side?

Back

Each side is 30 inches, since the perimeter is divided equally among the three sides.

Front

What is the height of an equilateral triangle with a side length of 30 inches?

Back

The height is 15√3 inches.

Front

What is the value of 'x' in a 30-60-90 triangle if the hypotenuse is 50?

Back

x = 25, and the side opposite the 60° angle is 25√3.

Front

What is the value of 'y' in a 30-60-90 triangle if the side opposite the 30° angle is 8√3?

Back

y = 16.

Front

How do you calculate the area of a 30-60-90 triangle?

Back

Area = (1/2) * base * height. For a 30-60-90 triangle, Area = (1/2) * x * (x√3) = (√3/4) * x².

Front

What is the formula for the Pythagorean theorem?

Back

a² + b² = c², where 'c' is the hypotenuse and 'a' and 'b' are the other two sides.

Front

What is the value of 'x' if the side opposite the 60° angle is 19√3?

Back

x = 19.