The Pythagorean Theorem

Algebra 1Mrs. McGowan

Grand Canyon University

TEC 551

Learning Objectives

Today you will learn to apply the Pythagorean Theorem. You will know

you know this when you can find a side length of a right triangle given the

lengths of its other two sides, with 85% accuracy, and apply the Pythagorean Theorem to real-world problems with

80% accuracy.

The Pythagorean Theorem

Knowing how to apply the Pythagorean Theorem is an important skill in algebra. You will find that there are many real world applications to these skills that you might not have thought about. The Pythagorean Theorem is one of the most significant theorems in mathematics. To apply the theorem, you will need to use your knowledge of squares and square roots.

A Video on the Pythagorean Theorem

(2007)

Using the Pythagorean Theorem to Find the Missing Hypothenus

Use the Pythagorean Theorem to find the length of side c.

a2 + b2 = c2

32 + 42 = c2 Plug values into the formula9 + 16 = c2 Simplify the squared values 25 = c2 Simplify (add 9 and 16) 5 = c Take the square root of both sides of the equation

(2004)

Using the Pythagorean Theorem to Find the

Missing Lega2 + b2 = c2

a2 + 62 = 102 Plug values into the formulaa2 + 36 = 100 Simplify the squared valuesa2 + 36 = 100 Simplify (subtract 36 from both sides)a2 = 64 a = 8 Take the square root of both sides of the equation

(2004)

Solving a Real-World Pythagorean Theorem

Problem

a2 + b2 = c2

152 + 202 = c2 Plug values into the formula225 + 400 = c2 Simplify the squared values625 = c2 Simplify (add 225 and 400)25 = c Take the square root of both sides of the equation

Your boat is traveling due north at 20 miles per hour. A friend’s boat left at the same time from the same location and headed due west at 15 miles per hour. After an hour you get a call from your friend who tells you that he has just stopped because of engine trouble. How far must you travel to reach your friend?

(2004)

Independent Practice

Solve for y.

X = 20 X = 11

(2004)

Independent Practice

Solve for x.

X = 3.46X = 4.47

(2004)

Independent Practice

-

A baseball diamond is a square with sides of 90 feet. To the nearest foot, how long is a throw from third base to first base?

X = 127. 28 X = 124.25

(2004)

Independent Practice

A garden in the shape of a right triangle is represented by the figure at right. What is the length of the third side of the garden?

17.20 ft 9.8 ft

(2004)

References

Ellis, W., Hollowell, K. A., Kennedy, P. A., Schultz, J. E. (2004). Holt Algebra 1. New York, New York: Holt, Rinehart, and Winston, Inc.

ModuMath. (2007).Algebra: Pythagorean Theorem and Other Formulas [Full Video]. Available from http://www.discoveryeducation.com/

Correct!!

Next Problem

Incorrecta2 + b2 = c2

162 + 122 = c2 Plug values into the formula

256 + 144 = c2 Simplify the squared values

400 = c2 Simplify (add 256 and 144)

20 = c Take the square root of both sides of the equation

Next Problem

Correct!!

Next Problem

Incorrect

Next Problem

a2 + b2 = c2

22 + b2 = 42 Plug values into the formula4 + b2 = 16 Simplify the squared valuesb2 = 12 Simplify (subtract 4 from both sides)3.46 = c Take the square root of both sides of the equation

Correct!!

Next Problem

Incorrect

Next Problem

a2 + b2 = c2

902 + 902 = c2 Plug values into the formula8100 + 8100 = c2 Simplify the squared values16200 = c2 Simplify (add 8100 and 8100)127.28 = c Take the square root of both sides of the equation

Correct!!

Next

Incorrect

Next

a2 + b2 = c2

102 + b2 = 142 Plug numbers into formula100 + b2= 196 Simplify squared valuesb2 = 96 Simplify (subtract 100 from both sides)b = 9.8 ft Take the square root of both sides