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, such as 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?

Back

To find the hypotenuse, multiply the length of one leg by √2.

Front

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

Back

To find the longer leg, multiply the length of the shorter leg by √3.

Front

How do you determine if three lengths can form a right triangle?

Back

Use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

If the legs of a right triangle are 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

Can the lengths 15, 12, and 9 form a right triangle?

Back

Yes, because 15² = 12² + 9² (225 = 144 + 81).

Front

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

Back

Area = (1/2) * base * height.