Question 1210261
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Acute triangle  ABC  has   sin(A) = {{{2/5}}}   and   sin(B) = {{{2/sqrt(7)}}}.   What is  sin(C)  ?
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<pre>
Since sin(A) = {{{2/5}}}  and angle A is acute (given), we have

    A = {{{arcsin(2/5)}}} = 23.5781785 degrees.



Since sin(B) = {{{2/sqrt(7)}}}  and angle B is acute (given), we have

    B = {{{arcsin(2/sqrt(7))}}} = arcsin(0.755928946) = 49.1066053 degrees.



Therefore,  C = 180 - 23.5781785 - 49.1066053 = 107.3152162 degrees.


Then  sin(C) = 0.95468179116.


<U>ANSWER</U>.  sin(C)  is about  0.95468179116.
</pre>

Solved.



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<H3>A post-solution note</H3>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;As &nbsp;I &nbsp;solved the problem to the end, &nbsp;I see that its formulation 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is &nbsp;FATALLY &nbsp;INCORRECT &nbsp;and is &nbsp;SELF-CONTRADICTORY.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Indeed, &nbsp;the problem says that the given triangle is acute, 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;which means that all three its angles are acute.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;But the angle &nbsp;C, &nbsp;as &nbsp;I &nbsp;found it, &nbsp;is &nbsp;OBTUSE: &nbsp;&nbsp;its measure is about &nbsp;107 &nbsp;degrees.


<H3>So, &nbsp;this problem simply &nbsp;DECEIVES &nbsp;a reader,
which is &nbsp;{{{highlight(highlight(unacceptable))}}} &nbsp;for a &nbsp;Math problem.</H3>