Exploring Right Triangles and the Pythagorean Theorem

The video tutorial explains how to find the length of an unknown side in a right triangle using the Pythagorean theorem. It begins by identifying the given side lengths and the hypotenuse. The Pythagorean theorem is then applied to set up an equation, which is solved to find the unknown side. The process includes calculating the square of the given sides, subtracting to isolate the unknown side, and taking the square root to find its length. The tutorial concludes with an estimation of the square root to understand its approximate value.

What type of triangle is being discussed in the problem?

• Equilateral triangle

• Scalene triangle

• Isosceles triangle

• Right triangle

Which side of the triangle is known as the hypotenuse?

• Side 9

• Side a

• None of the above

• Side 14

According to the Pythagorean theorem, what is the relationship between the sides of a right triangle?

• a^2 + 9^2 = 14^2

• 9^2 + 14^2 = a^2

• None of the above

• a^2 + 14^2 = 9^2

What is the first step to solve for side a using the Pythagorean theorem?

• Multiply both sides by a

• Subtract 81 from both sides

• None of the above

• Add 81 to both sides

What is the value of 14 squared?

• 176

• 186

• 196

• 166

What is the result of subtracting 81 from 196?

• 125

• 115

• 95

• 105

What mathematical operation is used to find the value of a from a squared?

• Square root

• Subtraction

• Addition

• Multiplication

What is the square root of 115 approximately between?

• 12 and 13

• 11 and 12

• 9 and 10

• 10 and 11

Which of the following is a prime number found in the factorization of 115?

• Neither

• Both 5 and 23

• 23

• 5

Can the square root of 115 be factored further into smaller prime numbers?

• Yes

• No

• Only into 5

• Only into 23