Pythagorean Theorem and Triangle Properties

The video tutorial explains how to find the lengths of sides A and B in a right triangle with angles of 30 and 60 degrees, given that side C is 18. It uses the property of special triangles to determine that side A is half of side C, making A equal to 9. To find side B, the Pythagorean theorem is applied, resulting in B being approximately 15.6. The tutorial emphasizes the importance of symbolic rearrangement to minimize errors during calculations.

What are the angles in the right triangle discussed in the video?

• 30 and 60 degrees

• 45 and 45 degrees

• 60 and 90 degrees

• 30 and 90 degrees

What is the sum of the angles in a triangle?

• 270 degrees

• 180 degrees

• 360 degrees

• 90 degrees

In a right triangle, what is the angle opposite the hypotenuse?

• 60 degrees

• 30 degrees

• 90 degrees

• 45 degrees

What is the special property of the side opposite the 30-degree angle in a right triangle?

• It is twice the length of the hypotenuse

• It is equal to the other leg

• It is half the length of the hypotenuse

• It is equal to the hypotenuse

What is the relationship between the sides in a 30-60-90 triangle?

• The side opposite 30 degrees is equal to the hypotenuse

• The side opposite 60 degrees is equal to the hypotenuse

• The side opposite 60 degrees is half the hypotenuse

• The side opposite 30 degrees is half the hypotenuse

If the hypotenuse is 18, what is the length of side 'a'?

• 6

• 12

• 9

• 18

What is the value of 'a' if 'c' is 18 in a 30-60-90 triangle?

• 18

• 9

• 12

• 6

Which theorem is used to find the length of side 'B'?

• Cosine rule

• Sine rule

• Pythagorean theorem

• Thales' theorem

What is the formula for the Pythagorean theorem?

• b^2 - a^2 = c^2

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + c^2 = b^2

How do you rearrange the Pythagorean theorem to solve for side 'B'?

• B = c^2 - a^2

• B = sqrt(c^2 + a^2)

• B = sqrt(c^2 - a^2)

• B = a^2 + c^2