Pythagorean’s Theorem

• https://www.youtube.com/watch?v=YompsDlEdtc

Movie Clip Questions • What is a practical (real world) application of Pythagorean’s

Theorem?

• When did Pythagoras live?

• Did Pythagoras invent the Pythagorean Theorem?

• How old is the Babylonian Tablet that lists 15 sets of Pythagorean numbers?

• What set of Pythagorean numbers did ancient Egyptian surveyors use?

• What type of strategy/proof did Pythagoras use to prove the Pythagorean Theorem?

• The Pythagorean Theorem has more than _______ proofs.

Some Vocabulary… Right Triangle:

Hypotenuse:

Legs:

Need to Know…

• What do you need to know about a right triangle in order to be able to use the Pythagorean theorem?

Let’s Practice

3

6

• First, label the triangle’s sides. Then, use Pythagorean’s Theorem to solve for the missing side of the triangle.

5

12

26

8

57

15

21

9

Competitive Tic-Tac-Toe

Trig review

Some Vocabulary… Right Triangle: Hypotenuse:

Angle: Opposite:

Side and Angle Relationship: Adjacent:

Labeling Triangles Practice • Label the sides of the following right triangles, using the angle given.

A

A

A

B

B

Setting up SOH CAH TOA • SOH CAH TOA is the key to setting up all Trig

equations.

• The first letter tells you which function is being used for that equation.

• The second letter tells you which side is the numerator of the equation.

• The third letter tells you which side is the denominator of the equation.

SOH CAH TOA

sin 𝜃 =𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 cos(𝜃) =

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 tan 𝜃 =

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

SOH CAH TOA Practice • Looking at what information is given for each of the right triangles

below, determine which function would be best to use to set up an equation.

x

x x

x

x

30°

70°

23°

3 5

8

12

45

9

13

Solving the Equations sin 𝑥 =

3

5 tan 30 =

8

𝑥 cos 70 =

𝑥

12

tan 23 =𝑥

45 sin 𝑥 =

9

13

SOH CAH TOA Practice

• Complete 2 Bingo’s and then turn it in.