Podcast
Questions and Answers
What does the Pythagorean Theorem state about the relationship between the sides of a right triangle?
What does the Pythagorean Theorem state about the relationship between the sides of a right triangle?
- The hypotenuse is always half the length of the longest side.
- The square of the hypotenuse is equal to the sum of the squares of the other two sides. (correct)
- The sum of the two shorter sides is equal to the hypotenuse.
- The length of each side must be the same.
In the example provided, what are the lengths of sides AB and BC used in the calculation?
In the example provided, what are the lengths of sides AB and BC used in the calculation?
- 9 cm and 12 cm
- 8 cm and 5 cm (correct)
- 10 cm and 3 cm
- 6 cm and 4 cm
How do you find the length of the diagonal AC using the Pythagorean Theorem?
How do you find the length of the diagonal AC using the Pythagorean Theorem?
- By taking the square root of the sum of the squares of AB and BC (correct)
- By adding the lengths of sides AB and BC
- By subtracting the shorter side from the longer side
- By multiplying the lengths of sides AB and BC
What is the calculated value of AC² in the example provided?
What is the calculated value of AC² in the example provided?
What is the approximate length of diagonal AC after performing the calculations?
What is the approximate length of diagonal AC after performing the calculations?
Flashcards
Pythagorean Theorem
Pythagorean Theorem
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Hypotenuse
Hypotenuse
The longest side of a right-angled triangle, opposite the right angle.
Right-angled triangle
Right-angled triangle
A triangle with one angle measuring 90 degrees.
Pythagorean Theorem Formula
Pythagorean Theorem Formula
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Finding missing side length
Finding missing side length
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Study Notes
Pythagorean Theorem Explained
- The example uses a rectangle ABC with sides AB = 8 cm and BC = 5 cm.
- We are asked to find the length of the diagonal AC, which is also the hypotenuse of the right triangle ABC.
- The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
- The formula is: hypotenuse² = side1² + side2²
- The sides AB and BC are known, so we can plug them into the formula: AC² = AB² + BC²
- The values are substituted: AC² = 8² + 5²
- The calculations are made: AC² = 64 + 25 = 89
- To find the length of AC, we take the square root of both sides: AC = √89
- The final answer is that AC is approximately 9.4 cm.
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