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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Cumulative Standards Review

Exercise 14 Page 540

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

42.3

Practice makes perfect

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

To find the missing side length, we will start by drawing a diagram to illustrate the situation.

We know that the lengths of AC and BC are 32 and 15, respectively. We also know that their included angle has a measure of 124^(∘). With this information, and using the Law of Cosines, we can write an equation to find AB.

AB^2= 15^2+ 32^2-2( 15)( 32)cos 124^(∘)

▼

Solve for AB

Calculate power

AB^2=225+1024-2(15)(32)(cos 124^(∘))

Use a calculator

AB^2=225+1024-2(15)(32)(- 0.55919290347...)

Multiply

AB^2=225+1024-(-536.825187332 )

a-(- b)=a+b

AB^2=225+1024+536.825187332

Add terms

AB^2=1785.82518733 ...

sqrt(LHS)=sqrt(RHS)

AB=sqrt(1785.82518733 ...)

Calculate root

AB=42.2590249217 ...

Round to 1 decimal place(s)

AB=42.3

Subchapter links

Exercises p.538-540