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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 5 Page 674

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

8.3

Practice makes perfect

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

Consider the given triangle.

We know the length of two sides, 14.7 and 7, and that the measure of their included angle is 18^(∘). 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= 7^2+ 14.7^2-2( 7)( 14.7)cos 18^(∘)

▼

Solve for x

Calculate power

x^2=49+216.09-2(7)(14.7)cos 18^(∘)

Use a calculator

x^2=49+216.09-2(7)(14.7)(0.951056...)

Multiply

x^2=49+216.09-195.727324...

Add and subtract terms

x^2=69.362676...

sqrt(LHS)=sqrt(RHS)

x=sqrt(69.362676...)

Calculate root

x=8.328425...

Round to 1 decimal place(s)

x≈ 8.3

Note that we only kept the principal root when solving the equation because x is the length of a side.

Subchapter links

Exercises p.674-679