Special Right Triangles.FA1

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 is the side length ratio 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 is the side length ratio of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1:√3:2.

Front

If the legs of a 45-45-90 triangle are each 18, what is the length of the hypotenuse?

Back

The hypotenuse is 18√2.

Front

If the shorter leg of a 30-60-90 triangle is 7, what is the length of the longer leg?

Back

The longer leg is 7√3.

Front

How do you find the length of the diagonal of a square?

Back

The diagonal of a square can be found using the formula d = s√2, where s is the side length.

Front

If the diagonal of a square is 13 m, what is the side length?

Back

The side length is approximately 9.19 m.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by the formula A = 1/2 * base * height.

Front

In a 30-60-90 triangle, if the shorter leg is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 8.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that 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).