Special Right Triangles

Front

What is a special right triangle?

Back

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

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.

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.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle if one leg is 5?

Back

The hypotenuse is 5√2.

Front

How do you find the length of the longer leg in a 30-60-90 triangle if the shorter leg is 4?

Back

The longer leg is 4√3.

Front

What is the formula to find the area of a right triangle?

Back

Area = 1/2 * base * height.

Front

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

Back

The hypotenuse is 6√2.

Front

In a 30-60-90 triangle, if the hypotenuse is 10, what is the length of the shorter leg?

Back

The shorter leg is 5.

Front

What is the relationship between the angles in a right triangle?

Back

The sum of the angles in a right triangle is always 180 degrees, with one angle being 90 degrees.

Front

How can you determine if a triangle is a special right triangle?

Back

Check if the angles are 30-60-90 or 45-45-90, or if the side ratios match those of special right triangles.