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Chapter 8: Q. 3 (page 555)

In Problems 3鈥�5, use the given information to determine the three remaining parts of each triangle.

Short Answer

Expert verified

The missing values area=18,B鈮�48.09掳, andC=79.9掳

Step by step solution

01

Step 1. Given information

The given triangle is

02

Step 2. Use the Rule of Cosines 

  • By the rule of cosines, a2=b2+c2-2bccosA
  • Substitute the values b=17,c=19,A=52掳 to find the value of a.

a2=172+192-2(17)(19)cos(52)鈮�289+361-397.72鈮�324.28a鈮�18

03

Step 3. Use the rule of Sines

  • According to the rule of sines, sinAa=sinBb=sinCc.
  • Substitute b=17,a=18,A=52掳 into the formula and find the value of angle B.

sin(52)18=sinB17sinB=17脳0.78818B鈮�48.09

04

Step 4. Use Angle sum Property

The sum of angles of a triangle is 180掳.

So,C=180掳-52掳-48.09掳=79.9掳

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