SOLUTION: An oblique triangle has a side a= 6.5 in , side b = 6.0 in. and side c =3.5 in Find the value of angle A.

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Question 113638This question is from textbook
: An oblique triangle has a side a= 6.5 in , side b = 6.0 in. and side c =3.5 in Find the value of angle A. This question is from textbook

Answer by MathLover1(20850) About Me  (Show Source):
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+a=6.5in+, +b+=6.0in+, and +c+=3.5in+.
Determine the value of angle A.

The basic relationships among sides and angles of an oblique triangle are given by the Law of Sines and the Law of Cosines. When three parts (including a side) of an oblique triangle are given, the Law of Sines or the Law of Cosines can be used to solve the triangle.
The solution to all oblique triangles can also be found with one or more of the following three equations, plus the equation "180%5Eo+=+A+%2B+B+%2B+C", where a, b, and c are the sides opposite the angles A, B, and C (respectively):
Law of Sines: a+%2F+sin%28A%29+=+b+%2F+sin%28B%29+=+c+%2F+sin%28C%29
Law of Cosines:
a2+=+b2+%2B+c2+-+2bc+cos%28A%29
b2+=+c2+%2B+a2+-+2ca+cos%28B%29
c2+=+a2+%2B+b2+-+2ab+cos%28C%29

We will use:
a%5E2+=+b%5E2+%2B+c%5E2+-+2bc+cos%28A%29
+%286.5in%29%5E2=%286.0in%29%5E2+%2B+%283.5in%29%5E2+-+2%286.0in%29%283.5in%29+cos%28A%29
+42.25in%5E2=+36.0in%5E2+%2B+12.25in%5E2+-+42in%5E2cos%28A%29
+42.25in%5E2=+48.25+in%5E2+-+42in%5E2cos%28A%29
+42.25+in%5E2+-+48.25+in%5E2=+-+42in%5E2cos%28A%29
+-+6+in%5E2+=+-+42in%5E2cos%28A%29...... divide both sides by -1+in%5E2

++6++=+42cos%28A%29………
++cos%28A%29+=+6%2F42+………
++cos%28A%29+=+0.0034………
A+=++89.8%5Eo