Pythagorean Review

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). Formula: a² + b² = c².

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 unknown side if the hypotenuse is 10 and one side is 6?

Back

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

Front

How do you simplify √(a²)?

Back

√(a²) simplifies to |a| (the absolute value of a).

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

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 a leg.

Front

If the lengths of the two legs of a right triangle are both 5, what is the length of the hypotenuse?

Back

√(5² + 5²) = √(25 + 25) = √50 = 5√2.

Front

What is the value of x in the equation 3² + x² = 12²?

Back

x = √(12² - 3²) = √(144 - 9) = √135 = 3√15.

Front

What is the area of a right triangle with legs of length 6 and 8?

Back

Area = (1/2) * base * height = (1/2) * 6 * 8 = 24.

Front

What is the distance between the points (3, 4) and (0, 0)?

Back

Distance = √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5.