Pythagorean Theorem

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 is expressed as: c² = a² + b².

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the length of the missing side if the hypotenuse is 10 and one side is 6?

Back

8 (Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

Front

In a right triangle, if the lengths of the two legs are equal, what is the relationship between the legs and the hypotenuse?

Back

If the legs are equal (let's say both are 'a'), then the hypotenuse (c) can be found using c = a√2.

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: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a rectangular field is 50 yards wide and 100 yards long, how do you find the diagonal distance across the field?

Back

Use the Pythagorean Theorem: d = √(50² + 100²) = √(2500 + 10000) = √12500 = 111.8 yards.

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° angle is 'x', the side opposite the 60° angle is 'x√3', and the hypotenuse is '2x'.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

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

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

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

Back

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