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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. The Law of Sines and Law of Cosines

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Exercise 23 Page 675

The Law of Cosines relates the cosine of each angle in a triangle to its side lengths.

3.8

Practice makes perfect

For any △ ABC, the Law of Cosines relates the cosine of each angle to the side lengths of the triangle.

Let's use this law to find the value of x. Consider the given triangle.

We know the length of two sides, 3.0 and 1.2, and that the measure of their included angle is 123^(∘). With this information, we want to find the length of the third side x. We can use the Law of Cosines to write an equation in terms of x.

x^2=( 1.2)^2+( 3.0)^2-2( 1.2)( 3.0)cos 123^(∘)

▼

Solve for x

Calculate power

x^2=1.44+9.0-2(1.2)(3.0)cos 123^(∘)

Use a calculator

x^2=1.44+9.0 - 2(1.2)(3.0)(- 0.544639...)

Multiply

x^2= 1.44 +9.0-(- 3.921401...)

a-(- b)=a+b

x^2=1.44 +9.0 + 3.921401...

Add terms

x^2=14.361401...

sqrt(LHS)=sqrt(RHS)

x=sqrt(14.361401...)

Calculate root

x=3.789643...

Round to 1 decimal place(s)

x≈ 3.8

Note that we only kept the principal root when solving the equation, because x is the length of a side which means it will measure about 3.8 units.

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Exercises p.674-679