MMA Midterm Review #2

Front

What is the Pythagorean Theorem?

Back

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

How do you find the length of a missing side in a right triangle?

Back

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

Front

If one side of a right triangle is 6 feet and the other is 8 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 6² + 8² = c²; 36 + 64 = c²; 100 = c²; c = 10 feet.

Front

What is the definition of a right triangle?

Back

A triangle that has one angle measuring 90 degrees.

Front

What is the formula for calculating the area of a triangle?

Back

Area = 1/2 * base * height.

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 definition of a hypotenuse?

Back

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

Front

If the lengths of two sides of a right triangle are 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 5² + 12² = c²; 25 + 144 = c²; 169 = c²; c = 13.

Front

What is the definition of a ladder problem in geometry?

Back

A ladder problem typically involves finding the length of a ladder leaning against a wall, forming a right triangle with the wall and the ground.

Front

How do you calculate the length of a ladder leaning against a wall?

Back

Use the Pythagorean Theorem: if the foot of the ladder is d feet from the wall and the height h feet up the wall, then the length of the ladder L is given by L = √(d² + h²).