The Pythagorean Theorem

By: Ms. Kayla Van Auken

10th Grade

02/17/2010

Objectives

In this lesson, you will learn how to….

 • prove the Pythagorean Theorem• demonstrate Pythagorean Identities can be used

to show they are equivalent to the Pythagorean Theorem

• use Pythagorean Theorem to solve real world problems

“University of Luxembourg, 2004”

Review Quiz

1. Who was Pythagoras and what does the Pythagorean Theorem state?

2. What are the three types of right triangles?

3. How do we calculate sine, cosine, and tangent?

4. How do we calculate missing sides or angles of a triangle?

Answers

1. Pythagoras- mathematician credited with creating the Pythagorean Theorem a2+b2=c2

2. 3-4-5, 30-60-90, and 45-45-90

3. SOH-CAH-TOA

4. sine, cosine, and tangent

ReviewRight Triangles:• 3-4-5 Triangle

• 45º-45º-90º Triangle

• 30º-60º-90º Triangle• Special Right Triangles

“onlinemathlearning.com , 2008”

Review

SOH-CAH-TOA• Sin A= Opposite / Hypotenuse• Cos A= Adjacent / Hypotenuse• Tan A= Opposite / Adjacent• SOH-CAH-TOA

“Mudhar, 2007”

ReviewMissing sides and angles use:• Sin A= a/c • Cos A= b/c• Tan A= a/b • Sin B= b/c • Cos B= b/a• Tan B= b/a• a² + b² = c²“Mudhar, 2007”

Example

• A ladder 5 m long, leaning against a vertical wall makes an angle of 65˚ with the ground.

a) How high on the wall does the ladder reach?

b) How far is the foot of the ladder from the wall?

“onlinemathlearning.com , 2008”

Answers

a) sin 65˚= PQ/5

PQ = sin 65˚ × 5 = 4.53 m

b) cos 65˚= RQ/5

RQ = cos 65˚ × 5 = 2.11 m

onlinemathlearning.com (2008)

History

• Pythagoras • Specialties• followers / students• Group Discussion: Did he create the

Pythagorean Theorem?

The Pythagorean Theorem

• a2+b2=c2

• Pythagorean Theorem Proof

“Michaud, 2009”

The Pythagorean Identities

• sin²θ + cos²θ   =   1   • 1 + tan²θ   =   sec²θ   • 1 + cot²θ   =   csc ²θ

Note: explanation on how to obtain on white board

Real World Application

Apply the Pythagorean Theorem/Identities to:• find the height of a building• calculate how far away your friend is• find the measurement of your TV• calculate the angle of the ramp on the

moving truck

Homework

• Page 371 in your textbook problems 2-46 even

• Due upon completion of projects

Now

• Get in small groups • Solve problems independently then share

answers and processes• Think of ways to remember formulas• Quiz

References

onlinemathlearning.com (2008). Trigonometry Applications. Retrieved from http://www.onlinemathlearning.com/