Solve for Unknown Side Lengths Using the Pythagorean Theorem

This video tutorial teaches how to solve for unknown side lengths in right triangles using the Pythagorean theorem. It begins with a review of the theorem, explaining the relationship between the sides of a right triangle. The tutorial then covers how to create equations using the theorem and solve for unknown sides, including working with square roots. Two examples are provided: one involving a triangle with given side lengths and another involving distances between cities. The video concludes by addressing common misunderstandings about solving right triangles.

What does the Pythagorean theorem state about the sides of a right triangle?

• The hypotenuse is always the longest side.

• The sum of the squares of the legs equals the square of the hypotenuse.

• The triangle has two equal sides.

• The sum of the angles is 180 degrees.

How can you express the Pythagorean theorem in terms of an equation?

• A^2 - B^2 = C^2

• A^2 = B^2 + C^2

• A^2 + B^2 = C^2

• A + B = C

What is the square root of 16?

• 4

• 3

• 2

• 5

In the example with a right triangle having sides 8 and 15, what is the length of the hypotenuse?

• 17

• 19

• 21

• 13

What is the first step in solving for an unknown side length in a right triangle?

• Check the answer.

• Write an equation using the Pythagorean theorem.

• Find the square root of the hypotenuse.

• Measure the sides directly.

In the city distance example, what is the distance from Metro City to Excalibur?

• 25 miles

• 10 miles

• 15 miles

• 20 miles

Why is it not possible to solve for two unknown side lengths using the Pythagorean theorem?

• It only works for equilateral triangles.

• The theorem requires knowledge of all angles.

• You need at least two known side lengths to apply the theorem.

• The theorem only applies to isosceles triangles.