Pythagorean Theorem and Applications

Pythagorean Theorem and Applications

How does Pythagorean Theorem help us?

What is Pythagorean Theorem?

A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.

But what does it do for us?

Pythagorean Theorem allows us to find unknown measures of side lengths for right triangles.

Right Triangles

These always have three sides - two legs and a hypotenuse. The two legs are always shorter than the hyptenuse and the hypotenuse is always found across from the right angle.

Multiple Choice

What is the longest side of a right triangle called?

• Leg A
• Leg B
• Hypotenuse
• Pythagoras' Big Buddy

Multiple Choice

The hyopotenuse of the triangle measures

• 32

• 24

• 40

• 32 and 24

Multiple Choice

The hypotenuse of the following triangle measures

• 28

• 23

Multiple Choice

Find the value of x.

• 7
• 8
• 9
• 10

Multiple Choice

^{Find the missing side (hint: use what you know about estimating irrational numbers to answer)}

• 9

• 41

• 6.4

• 6.2

Distance Between Two Points

We can use the slope between two points to create the legs of a right triangle.

Distance Between Two Points

• We can count the rise and the run.

• That will become the legs of the right triangle we are creating.

• Using Pythagorean Theorem, we can determine the distance between the two points by finding the length of the missing hypotenuse.

Multiple Choice

Find the distance.

• 7.1
• 7.8
• 8.7
• 8.9

Multiple Choice

What is the distance between the two points?

• 6.3
• 6.5
• 6.7
• 16

Pythagorean Theorem in the Real-World

-We can use Pythagorean Theorem to do more than just find the hypotenuse of right triangles and the distance between two points.

-We can apply those skills to do things like find out how long things like shadows are, how tall buildings are, or find the shortest distance to a place.

Multiple Choice

A 14-foot ladder is set up 4 feet from the base of a building.  How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.

• 13.4 feet
• 14.6 feet
• 16.5 feet
• 18.0 feet

Multiple Choice

Brianna is planting a sapling. The garden center recommended she stabilize the sapling with guide wires for the first year.

• 6.6 feet

• 7.8 feet

• 12.2 feet

• 15.6 feet