Pythagorean Theorem and Applications

This video tutorial covers two application problems that can be solved using the Pythagorean Theorem. The first problem involves calculating the length of a ramp for a porch, while the second problem involves finding the hypotenuse of a sailboat's sail. The video provides a step-by-step guide on how to apply the Pythagorean Theorem to these real-world scenarios, including substituting values, simplifying equations, and calculating square roots. The tutorial concludes with a summary of the key points discussed.

What is the formula for the Pythagorean Theorem?

• a + b = c^2

• a^2 + b^2 = c

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

In the first problem, what is the height of the porch from the ground?

• 5 feet

• 15 feet

• 3 feet

• 12 feet

How far must the ramp start from the base of the porch in the first problem?

• 8 feet

• 12 feet

• 15 feet

• 10 feet

What is the approximate length of the ramp calculated in the first problem?

• 13.5 feet

• 14.2 feet

• 12.4 feet

• 11.3 feet

In the second problem, what is the height of the sail?

• 12 feet

• 15 feet

• 10 feet

• 8 feet

What is the length of the bottom edge of the sail in the second problem?

• 12 feet

• 8 feet

• 15 feet

• 10 feet

What is the length of the hypotenuse of the sail calculated in the second problem?

• 17 feet

• 15 feet

• 18 feet

• 16 feet

Which of the following is a perfect square?

• 153

• 144

• 289

• 225

What is the principal square root of 289?

• 18

• 16

• 17

• 15

Why do we take the principal square root when solving for c in the Pythagorean Theorem?

• Because c can be negative

• Because c must be positive

• Because c is always zero

• Because c is a variable