Question 87186
<pre><b><font size = 4>
Determine the measure of side a given the 
following informaiton for triangle ABC: 
C = 25degrees, B = 108degrees, c = 59ft
{{{drawing(300,357,-10,100,-10,40,
triangle(0,0,59,0,90.5510328,33.83434035),    
locate(-5,3,A), locate(63,3,B), locate(93,35,C),  
locate(76,28,"25°"), locate(48,3,"108°"), locate(73,15,"a"),
locate(30,-2,"c=59"), locate(37,20,"b")
)}}}

First we find angle A using

A + B + C = 180°

A + 108° + 25° = 180°

A + 133° = 180°

A = 47°

{{{drawing(300,357,-10,100,-10,40,
triangle(0,0,59,0,90.5510328,33.83434035),    
locate(-5,3,A), locate(63,3,B), locate(93,35,C),  
locate(76,28,"25°"), locate(48,3,"108°"), locate(73,15,"a"),
locate(30,-2,"c=59"), locate(37,20,"b"), locate(9,3,"47°")
)}}}

Now we use the law of sines:

{{{a/sin(A)}}} = {{{b/cos(B)}}} = {{{c/sin(C)}}}

We only need

{{{a/sin(A)}}} = {{{c/sin(C)}}}

Solve for c:

Cross multiply:

{{{a*sin(C)}}} = {{{c*sin(A)}}}

Divide both sides by {{{sin(C)}}}

{{{a}}} = {{{(c*sin(A))/sin(C)}}} 

     59*sin(47°)
a = -------------
       sin(25°)

a = 102.1012869 ft.

Since the angles are measured to the 
nearest degree, and the side c measured to
2 significant digits, then side a
should be rounded to either 102 ft. or 100 ft. 

Edwin</pre>