Question 1181689
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            There are 2 (two) ways to solve the problem.


            One way is to use the cosine law.


            Another way is via the area.


            I will show you this second way.



<pre>
Calculate the area of the triangle, using the Heron's formula.


Doing this way, you get for the area of the triangle the value of 101.666  cm^2.


The area of the triangle also can be found using the formula


    area = {{{(1/2)*14*19*sin(alpha)}}},


where {{{alpha}}}  is the angle between the sides  of  14 and 19 cm.


So,  {{{(1/2)*14*19*sin(alpha)}}} = 101.666 


It gives  {{{sin(alpha)}}} = {{{(2*101.666)/(14*19)}}} = 0.764.


Also, notice that  14^2 + 19^2 = 557 < 900 = 30^2.


Hence, the angle {{{alpha}}} must be acute.


It gives for {{{alpha}}}  the unique answer  


    {{{alpha}}} = arcsin(0.764) = 0.86949 radians = 49.8 degrees   (rounded as requested).
</pre>

Solved.


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So, having two ways to express / (to calculate) the area, we obtain the equation to find the sine of the angle.


From equation, we determine the sine of the angle and then the angle itself.