special right triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths. The two main types are the 30-60-90 triangle and the 45-45-90 triangle.

Front

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

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2. The shortest side (opposite the 30° angle) is 'x', the longer leg (opposite the 60° angle) is 'x√3', and the hypotenuse is '2x'.

Front

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

Back

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

Front

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

Back

To find the hypotenuse, double the length of the shortest side (the side opposite the 30° angle). If the shortest side is 'x', then the hypotenuse is '2x'.

Front

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

Back

To find the longer leg (the side opposite the 60° angle), multiply the length of the shortest side (the side opposite the 30° angle) by √3. If the shortest side is 'x', then the longer leg is 'x√3'.

Front

What is the formula for the diagonal of a square?

Back

Front

If the diagonal of a square is 18, what is the side length?

Back

Front

In a 45-45-90 triangle, if one leg is 8, what is the length of the hypotenuse?

Back

Front

What is the Pythagorean theorem?

Back

Front

Back