Pythagorean Theorem (Word Problems)

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle, typically referred to as sides 'a' and 'b'.

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as: a² + b² = c².

Front

How do you calculate the distance between two points using the Pythagorean Theorem?

Back

To calculate the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, you can use the formula: distance = √((x2 - x1)² + (y2 - y1)²). This is derived from the Pythagorean Theorem.

Front

In the context of a ladder problem, how do you identify the legs and hypotenuse?

Back

In a ladder problem, the distance from the wall to the base of the ladder represents one leg (a), the height the ladder reaches on the wall represents the other leg (b), and the length of the ladder represents the hypotenuse (c).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem, which states that the sum of the squares of the two legs equals the square of the hypotenuse.

Front

How can you determine the length of the hypotenuse if you know the lengths of the legs?

Back

To determine the length of the hypotenuse (c) when you know the lengths of the legs (a and b), you can use the formula: c = √(a² + b²).

Front

What is the significance of the diagonal in a rectangle or TV screen problem?

Back

In a rectangle or TV screen problem, the diagonal represents the hypotenuse of a right triangle formed by the width and height of the rectangle. The relationship is given by the Pythagorean Theorem.

Front

What is the formula to find the width of a TV screen if the diagonal and height are known?

Back

If the diagonal (d) and height (h) of a TV screen are known, the width (w) can be found using the formula: w = √(d² - h²).

Front

What is the first step in solving a word problem involving the Pythagorean Theorem?

Back

The first step is to identify the right triangle in the problem and determine which sides correspond to the legs and which side corresponds to the hypotenuse.

Front

How do you set up an equation for a word problem involving distances?

Back

To set up an equation for a word problem involving distances, identify the known distances, assign variables to the unknowns, and apply the Pythagorean Theorem to relate the sides.