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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 17 Page 703

Use the Pythagorean Theorem.

9sqrt(3)≈ 15.6

Practice makes perfect

To find the missing side 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=x, b=9 and c=18.

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

a^2+b^2=c^2

SubstituteValues

Substitute values

x^2+ 9^2= 18^2

▼

Solve for x

Calculate power

x^2+81=324

LHS-81=RHS-81

x^2=243

sqrt(LHS)=sqrt(RHS)

x=sqrt(243)

SplitIntoFactors

Split into factors

x=sqrt(81 * 3)

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

x=sqrt(81)* sqrt(3)

Calculate root

x=9sqrt(3)

Use a calculator

x=15.58845...

Round to 1 decimal place(s)

x≈ 15.6

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