DashboardNewsSettingsHelp
Get Premium
Dashboard
Dashboard Sign out
McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
6. The Law of Sines and Law of Cosines
Continue to next subchapter
search

Exercise 22 Page 675

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

13.1

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 value of x. Consider the given triangle.

We know the length of two sides, 11.2 and 12.4, and that the measure of their included angle is 67^(∘). 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=( 12.4)^2+( 11.2)^2-2( 12.4)( 11.2)cos 67^(∘)
â–¼
Solve for x
CalcPow

Calculate power

x^2=153.76+125.44-2(12.4)(11.2)cos 67^(∘)
UseCalc

Use a calculator

x^2=153.76+125.44-2(12.4)(11.2)(0.390731...)
Multiply

Multiply

x^2=153.76+125.44-108.529442...
AddSubTerms

Add and subtract terms

x^2=170.670558...
SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(170.670558...)
CalcRoot

Calculate root

x=13.064094...
RoundDec

Round to 1 decimal place(s)

x≈ 13.1

Note that we only kept the principal root when solving the equation, because x is the length of a side which means it will be measured about 13.1 units.

Subchapter links expand_more
arrow_right Exercises p.674-679
1
Exercises 2 (Page 674)
Exercises 3 (Page 674)
Exercises 4 (Page 674)
Exercises 5 (Page 674)
Exercises 6 (Page 674)
Exercises 7 (Page 674)
Exercises 8 (Page 674)
Exercises 9 (Page 674)
Exercises 10 (Page 674)
Exercises 11 (Page 674)
Exercises 12 (Page 675)
Exercises 13 (Page 675)
Exercises 14 (Page 675)
Exercises 15 (Page 675)
Exercises 16 (Page 675)
Exercises 17 (Page 675)
Exercises 18 (Page 675)
Exercises 19 (Page 675)
Exercises 20 (Page 675)
Exercises 21 (Page 675)
Exercises 22 (Page 675)
Exercises 23 (Page 675)
Exercises 24 (Page 675)
Exercises 25 (Page 675)
Exercises 26 (Page 675)
Exercises 27 (Page 675)
Exercises 28 (Page 675)
Exercises 29 (Page 676)
Exercises 30 (Page 676)
Exercises 31 (Page 676)
Exercises 32 (Page 676)
Exercises 33 (Page 676)
Exercises 34 (Page 676)
Exercises 35 (Page 676)
Exercises 36 (Page 676)
Exercises 37 (Page 676)
Exercises 38 (Page 676)
Exercises 39 (Page 676)
Exercises 40 (Page 676)
Exercises 41 (Page 676)
Exercises 42 (Page 676)
Exercises 43 (Page 676)
Exercises 44 (Page 677)
Exercises 45 (Page 677)
Exercises 46 (Page 677)
Exercises 47 (Page 677)
Exercises 48 (Page 677)
Exercises 49 (Page 677)
Exercises 50 (Page 677)
Exercises 51 (Page 678)
Exercises 52 (Page 678)
Exercises 53 (Page 678)
Exercises 54 (Page 678)
Exercises 55 (Page 678)
Exercises 56 (Page 678)
Exercises 57 (Page 678)
Exercises 58 (Page 678)
Exercises 59 (Page 679)
Exercises 60 (Page 679)
Exercises 61 (Page 679)
Exercises 62 (Page 679)
Exercises 63 (Page 679)
Exercises 64 (Page 679)
Exercises 65 (Page 679)
Exercises 66 (Page 679)
Exercises 67 (Page 679)
Exercises 68 (Page 679)
Exercises 69 (Page 679)
Exercises 70 (Page 679)
Exercises 71 (Page 679)
Exercises 72 (Page 679)
Exercises 73 (Page 679)