Special Right Triangles (30-60-90 & 45-45-90)

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 a 45-45-90 triangle?

Back

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

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

If the shortest side (opposite the 30° angle) is 'x', then the lengths of the other sides are 'x√3' (opposite the 60° angle) and '2x' (hypotenuse).

Front

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

Back

If each leg of the triangle is 'x', then the hypotenuse is 'x√2'.

Front

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

Back

Multiply the length of the shortest side by 2.

Front

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

Back

Multiply the length of the shortest side by √3.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If the legs of a 45-45-90 triangle are each 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

Front

Which set of sides can form a right triangle? 4, 5, 6 or 5, 12, 13?

Back

5, 12, 13 can form a right triangle.