Special Right Triangles

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, if the shortest side (opposite the 30° angle) is 'x', then the side opposite the 60° angle is 'x√3', and the hypotenuse is '2x'.

Front

If the shortest side of a 30-60-90 triangle is 5, what are the lengths of the other sides?

Back

The side opposite the 60° angle is 5√3, and the hypotenuse is 10.

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are both 45 degrees and the right angle is 90 degrees. The sides are in the ratio 1:1:√2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if each leg is 'x', then the hypotenuse is 'x√2'.

Front

If each leg of a 45-45-90 triangle is 6, what is the length of the hypotenuse?

Back

The hypotenuse is 6√2.

Front

How do you find the length of a side in a 30-60-90 triangle?

Back

Use the ratios: if you know one side, multiply or divide by √3 or 2 to find the other sides.

Front

How do you find the length of a side in a 45-45-90 triangle?

Back

If you know the length of one leg, multiply it by √2 to find the hypotenuse.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

How can you find the area of a 30-60-90 triangle?

Back

Area = 1/2 * (shortest side) * (side opposite 60°) = 1/2 * x * (x√3) = (x^2√3)/2.