What is the relationship between the sides of a right triangle?

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, expressed as $$c^2 = a^2 + b^2$$ .

How do you simplify $$5\text{sqrt}(45a^3b^6c^5)$$ ?

The simplified form is $$15ab^3c^2\text{sqrt}(5ac)$$ .

What is the significance of the Pythagorean Theorem in real-life applications?

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

What is the formula for finding the area of a right triangle?

The area (A) of a right triangle can be calculated using the formula: $$A = \frac{1}{2} \times base \times height$$ .

What is the distance from the base of a 14ft ladder leaning against a barn that reaches 7ft high?

Using the Pythagorean Theorem: Distance = $$7\text{sqrt}(3) ft$$ .

What is the relationship between the sides of a scalene triangle?

In a scalene triangle, all sides and angles are different, and the Pythagorean Theorem does not apply unless it is a right triangle.

What is the difference between a right triangle and an obtuse triangle?

A right triangle has one angle equal to 90 degrees, while an obtuse triangle has one angle greater than 90 degrees.

How can you verify if three lengths can form a right triangle?

To verify, check if the lengths satisfy the Pythagorean Theorem: $$a^2 + b^2 = c^2$$ , where c is the longest side.

Pythagorean Theorem Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

3.

FLASHCARD QUESTION

Front

If a ladder is leaning against a wall, how can you find the distance from the base of the ladder to the wall?

Back

4.

FLASHCARD QUESTION

Front

What is a Pythagorean Triple?

Back

5.

FLASHCARD QUESTION

Front

Calculate the length of the diagonal of a rectangle with length 13m and width 16m.

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

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

Back

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