WED (12/4) M8 U.6 HW Pythag. Theorem (day 1)

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

What is a hypotenuse?

Back

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

Front

If one side of a right triangle is 8 m and the other side is 15 m, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17 m.

Front

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

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

Front

In a right triangle, if one angle is 90 degrees, what are the other two angles?

Back

The other two angles in a right triangle must add up to 90 degrees.

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.

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 use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: Distance = √((x2 - x1)² + (y2 - y1)²).

Front

If a rectangular pool measures 25 m by 50 m, how do you calculate the diagonal distance?

Back

Use the Pythagorean Theorem: Diagonal = √(25² + 50²) = √(625 + 2500) = √3125 = 55.9 m.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to determine distances and relationships between different points.