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McGraw Hill Integrated II, 2012
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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 26 Page 675

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

72

Practice makes perfect

For any â–³ 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 values of x. 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!

( 25.4)^2=( 13.5)^2+( 26.2)^2-2( 13.5)( 26.2)cos x^(∘)
â–¼
Solve for cos x^(∘)
CalcPow

Calculate power

645.16=182.25+686.44-2(13.5)(26.2)cos x^(∘)
AddTerms

Add terms

645.16=868.69-2(13.5)(26.2)cos x^(∘)
Multiply

Multiply

645.16=868.69-707.4cos x^(∘)
SubEqn

LHS-868.69=RHS-868.69

- 223.53=- 707.4cos x^(∘)
DivEqn

.LHS /(- 707.4).=.RHS /(- 707.4).

- 223.53/- 707.4=cos x^(∘)
DivNegNeg

- a/- b=a/b

223.53/707.4=cos x^(∘)
UseCalc

Use a calculator

0.315988...=cos x^(∘)
RearrangeEqn

Rearrange equation

cos x^(∘)=0.315988...



To find the value of x, we will use the inverse operation of cos, which is cos ^(- 1). cos x^(∘)= 0.315988... ⇕ x=cos ^(- 1)(0.315988...) Finally, we will use a calculator.

x=cos ^(- 1)( 0.315988...)
UseCalc

Use a calculator

x=71.579531...
RoundInt

Round to nearest integer

x≈ 72
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Exercises 2 (Page 674)
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