Triangle Measurements and Pythagorean Theorem

The video tutorial explains how to determine the base and height of a right triangle using the Pythagorean theorem. It starts by identifying the hypotenuse and defining the relationship between the base and height. The tutorial then applies the Pythagorean theorem to set up a quadratic equation, which is solved to find the base's length. Finally, the video demonstrates how to calculate and round the base and height to the nearest hundredth.

What is the hypotenuse of a right triangle?

• The side adjacent to the right angle

• The side forming the right angle

• The shortest side

• The side opposite the right angle

If the height is three more than twice the base, which expression represents the height?

• 3x + 2

• 2x + 3

• x + 3

• 3x + 2x

Which theorem is used to relate the sides of a right triangle?

• Pythagorean theorem

• Binomial theorem

• Fundamental theorem of algebra

• Quadratic theorem

What is the equation form of the Pythagorean theorem?

• A^2 + B^2 = C^2

• A + B = C^2

• A^2 + B^2 = C

• A^2 + B = C^2

What is the first step in solving the quadratic equation derived from the Pythagorean theorem?

• Factor the equation

• Simplify both sides

• Use the quadratic formula

• Set the equation to zero

What is the quadratic formula used to solve the equation?

• x = (-b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / 2a

• x = (b ± √(b^2 + 4ac)) / 2a

• x = (-b ± √(b^2 - 4ac)) / 2a

Why is only the positive solution of x considered in this problem?

• Because negative solutions are not allowed in algebra

• Because x is a length and must be positive

• Because the quadratic formula only gives positive solutions

• Because the problem specifies only positive numbers

What is the approximate length of the base of the triangle?

• 6.00 ft

• 5.83 ft

• 3.82 ft

• 1.42 ft

What is the approximate height of the triangle?

• 6.00 ft

• 5.83 ft

• 3.82 ft

• 1.42 ft

Why is it important to round the final answer to the hundredths place?

• To avoid errors in the quadratic formula

• To match the problem's requirements

• To make calculations easier

• To ensure precision in measurement