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Envision Math 2.0: Grade 8, Volume 2

EM

Envision Math 2.0: Grade 8, Volume 2 View details

1. Understand the Pythagorean Theorem

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Exercise 4 Page 384

Use the Pythagorean Theorem.

sqrt(41) inches, or 6.4 inches

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 a=4 inches and b=5 inches.

Let's substitute these values into the formula.

a^2+b^2=c^2

a= 4, b= 5

4^2+ 5^2=c^2

▼

Solve for c

Calculate power

16+25=c^2

Add terms

41=c^2

sqrt(LHS)=sqrt(RHS)

sqrt(41)=c

Rearrange equation

c=sqrt(41)

Calculate root

c=6.403124 ...

Round to 1 decimal place(s)

c=6.4

We found that the length of the hypotenuse of a right triangle that has leg lengths of 4 and 5 inches is sqrt(41) inches, or 6.4 inches.

Subchapter links

Do You Understand? p.384

Do You Know How? p.384

Practice & Problem Solving p.385-386

Assessment Practice p.386