Question 783304
<pre>
The sides are a=5, b=6, c=7

{{{drawing(400,800/3,-1,8,-1,5,locate(1.4,2.3,b=6),locate(3.5,0,c=7),
locate(7,0,B), locate(4.3,4.6,C), red(arc(0,0,3,-3,0,45)),
locate(0,0,A), locate(5.7,2.3,a=5), triangle(0,0,7,0,6cos(.7751933733),6sin(.7751933733)) )}}}

The smallest angle is the one opposite the smallest side.

This is the case of SSS (side-side-side)

We use the law of cosines solved for the cosine:

cos(A) = {{{(b^2+c^2-a^2)/(2bc)}}}

cos(A) = {{{(6^2+7^2-5^2)/(2*6*7)}}}

cos(A) = {{{(36+49-25)/84}}}

cos(A) = {{{60/84}}}

cos(A) = {{{5/7}}}

Use the inverse cosine on your calculator

A = 44.4153086°

A = 44° to the nearest degree.

Edwin</pre>