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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 16 Page 703

Use the Pythagorean Theorem.

2sqrt(221)≈ 29.7

Practice makes perfect

To find the missing side of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with a=20, b=22, and c=x.

Let's substitute these values into the formula and solve for x.

a^2+b^2=c^2

SubstituteValues

Substitute values

20^2+ 22^2= x^2

▼

Solve for x

Calculate power

400+484=x^2

Add terms

884=x^2

sqrt(LHS)=sqrt(RHS)

sqrt(884)=x

Rearrange equation

x=sqrt(884)

SplitIntoFactors

Split into factors

x=sqrt(4 * 221)

sqrt(a* b)=sqrt(a)*sqrt(b)

x=sqrt(4)*sqrt(221)

Calculate root

x=2sqrt(221)

Use a calculator

x=29.73213...

Round to 1 decimal place(s)

x≈ 29.7

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

Subchapter links

1 Geometric Mean p.703

2 The Pythagorean Theorem and Its Converse p.703

3 Special Right Triangles p.704

4 Trigonometry p.704

5 Angles of Elevation and Depression p.705

6 The Law of Sines and Law of Cosines p.705

7 Vectors p.706

8 Dilations p.706