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.