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McGraw Hill Integrated II, 2012 View details

6. The Law of Sines and Law of Cosines

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Exercise 6 Page 674

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

48.3

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 three side lengths and want to find one of the interior angles of the triangle. We can use the Law of Cosines to write an equation in terms of x.

16.2^2= 20^2+ 19.6^2-2( 20)( 19.6)cos x^(∘)

▼

Solve for cos x^(∘)

CalcPow

Calculate power

262.44=400+384.16-2(20)(19.6)cos x^(∘)

Multiply

262.44=400+384.16-784cos x^(∘)

AddTerms

Add terms

262.44=784.16-784cos x^(∘)

SubEqn

LHS-784.16=RHS-784.16

- 521.72=- 784cos x^(∘)

DivEqn

.LHS /(- 784).=.RHS /(- 784).

- 521.72/- 784=cos x^(∘)

DivNegNeg

- a/- b=a/b

521.72/784=cos x^(∘)

CalcQuot

Calculate quotient

0.665459=cos x^(∘)

RearrangeEqn

Rearrange equation

cos x^(∘)=0.665459

To find the value of x, we will use the inverse operation of cos, which is cos ^(- 1). cos x^(∘)=0.665459 ⇕ x=cos ^(- 1)(0.665459) To do so, we will use a calculator.

x=cos ^(- 1)(0.665459)

UseCalc

Use a calculator

x=48.282437

RoundDec

Round to 1 decimal place(s)

x≈ 48.3

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Exercises p.674-679

Exercise 6 Page 674

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