Question 113594
An oblique triangle has:

 {{{A=68°}}}, {{{B= 79°}}}, 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/ sin A = b/ sin B = c/ sin C}}}

The sum of all angles is {{{180°}}}, and we will find third angle {{{C}}}


{{{A + B + C = 180°}}}

{{{68 + 79 + C = 180}}}


{{{147 + C = 180}}}

{{{C = 180  - 147}}}

{{{C = 33}}}


{{{c/ sin C = b/ sin B}}}

	
{{{c  = (b/ sin B) sin C }}}

{{{c  = (8ft/ sin 79) (sin 33)}}}
	
{{{sin (79) = 0.98162718344766}}} or {{{0.98}}}

{{{sin(33) = 0.54463903501503}}} or {{{0.54}}}

then

{{{c  = (8.0ft/ 0.98) (0.54)}}}

{{{c  = (8.16ft)( 0.54)}}}

{{{c  = 4.4ft}}}