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6. Solve, to the nearest 0.0001, for all possible AABC with: a. a= 6, b=8, and C=38°.

6. Solve, to the nearest 0.0001, for all possible AABC with: a. a= 6, b=8, and C=38°.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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find all possible triangle ABC with: a = 6, b=8, C=38degrees. There should be TWO triangles. 

6. Solve, to the nearest 0.0001, for all possible AABC with: a. a= 6, b=8, and C= 38°. b. a = 6, b=8, and A=38°.
Transcribed Image Text:6. Solve, to the nearest 0.0001, for all possible AABC with: a. a= 6, b=8, and C= 38°. b. a = 6, b=8, and A=38°.
Expert Solution
Step 1

a) Given data:

  • Measure of side a=6
  • Measure of side b=8
  • Measure of angle C=38°

This case is called an ambiguous case.

Advanced Math homework question answer, step 1, image 1

Step 2

Using the law of cosines,

c2=a2+b2-2abcosC    =36+64-96cos38°    =100-75.64903235    =24.35097c  =4.9347

Using the law of sines,

asinA=bsinB=csinC

csin38°=8sinB

sinB=8×0.6156614754.9347

Step 3

          =4.9252918034.9347=0.9981

       B=sin-10.9981   =86.46749

Thus, this triangle is possible.

b) Given data:

  • a=6
  • b=8
  • A=38°

Using law of sines:

asinA=bsinB

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