SOLUTION: 14. An oblique triangle has A=68 degrees, B= 79 degrees, and b= 8.0 ft. Determine the length of side c.

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Question 113594This question is from textbook Mathematics for the Trades
: 14. An oblique triangle has A=68 degrees, B= 79 degrees, and b= 8.0 ft. Determine the length of side c. This question is from textbook Mathematics for the Trades

Answer by MathLover1(20850) About Me  (Show Source):
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An oblique triangle has:
A=68%B0, B=+79%B0, and b=+8.0+ft.
Determine the length of side c.
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.
There are four+possible+cases:
1. One side and two angles are given.
2. Two sides and one opposite angle are given.
3. Two sides and the included angle are given.
4. Three sides are given.
The Law+of+Sines is used in cases 1. and 2.
The Law+of+Cosines is used in cases III and IV.
LAW OF SINES
For any triangle ABC
a%2F+sin+A+=+b%2F+sin+B+=+c%2F+sin+C
The sum of all angles is 180%B0, and we will find third angle C

A+%2B+B+%2B+C+=+180%B0
68+%2B+79+%2B+C+=+180

147+%2B+C+=+180
C+=+180++-+147
C+=+33

c%2F+sin+C+=+b%2F+sin+B

c++=+%28b%2F+sin+B%29+sin+C+
c++=+%288ft%2F+sin+79%29+%28sin+33%29

sin+%2879%29+=+0.98162718344766 or 0.98
sin%2833%29+=+0.54463903501503 or 0.54
then
c++=+%288.0ft%2F+0.98%29+%280.54%29
c++=+%288.16ft%29%28+0.54%29
c++=+4.4ft