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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

2. The Pythagorean Theorem

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Exercise 2 Page 382

Use the Pythagorean Theorem.

1/2inches

Practice makes perfect

To find the missing side length of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2

In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with b= 310inches and a= 25inches.

Let's substitute these values into the formula.

a^2+b^2=c^2

a= 2/5, b= 3/10

( 2/5)^2+( 3/10)^2=c^2

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Solve for c

(a/b)^m=a^m/b^m

2^2/5^2+3^2/10^2=c^2

Calculate power

4/25+9/100=c^2

a/b=a * 4/b * 4

4 * 4/25 * 4+9/100=c^2

Multiply

16/100+9/100=c^2

Add fractions

16+9/100=c^2

Add terms

25/100=c^2

a/b=.a /25./.b /25.

25/25/100/25=c^2

Calculate quotient

1/4=c^2

sqrt(LHS)=sqrt(RHS)

sqrt(1/4)=c

Rearrange equation

c=sqrt(1/4)

sqrt(a/b)=sqrt(a)/sqrt(b)

c=1/sqrt(4)

Calculate root

c=1/2

Since a negative side length does not make sense, we only need to consider positive solutions.

Subchapter links

Try It p.382-384

Self-Assessment for Concepts & Skills p.384

Self-Assessment for Problem Solving p.385

Review & Refresh p.386

Concepts, Skills, & Problem Solving p.386-388