Pythagorean Word Problems

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). It can be expressed as: a² + b² = c².

Front

How do you identify the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is the formula to calculate the distance between two points in a coordinate plane?

Back

The distance d between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

In a right triangle, if one leg is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

Front

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

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30-degree angle is the shortest, the side opposite the 60-degree angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

You can use the Pythagorean Theorem. If the square of the length of the longest side equals the sum of the squares of the other two sides, then the triangle is a right triangle.

Front

What is the significance of the 3-4-5 triangle in geometry?

Back

The 3-4-5 triangle is a special right triangle where the sides are in the ratio 3:4:5. It is often used as a simple way to create a right angle.

Front

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

Back

You can rearrange the Pythagorean Theorem: if you know the lengths of the two legs (a and b), you can find the hypotenuse (c) using c = √(a² + b²). If you know one leg and the hypotenuse, you can find the other leg using a = √(c² - b²).

Front

What is the distance formula used for in real-world applications?

Back

The distance formula is used to calculate the straight-line distance between two points in various applications, such as navigation, construction, and computer graphics.

Front

How do you apply the Pythagorean Theorem to real-world problems?

Back

You can apply the Pythagorean Theorem to find distances in scenarios such as determining the length of a ladder needed to reach a certain height or calculating the distance between two locations.