Question 1129377
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{{{highlight(cross(The))}}} {{{highlight(cross(two))}}} {{{highlight(cross(sides))}}} {{{highlight(cross(of))}}} {{{highlight(cross(the))}}} Triangle ABC has sides AB=22cm and AC=8. If the area of the triangle 34.98 cm², what is it's perimeter?
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<pre>
Use the formula 


   Area = {{{(1/2)*a*b*sin(alpha)}}} for the area of a triangle, 


where "a" and "b" are two sides lengths and  {{{alpha}}}  is the angle between them.


Using given data, find {{{sin(alpha)}}}.


Having  {{{sin(alpha)}}},  find {{{cos(alpha)}}} = +/-{{{sqrt(1-sin^2(alpha))}}}.


    ===---> > > Notice that <U>there is NO NEED to find</U> {{{alpha}}} : <U>all you need is</U> {{{sin(alpha)}}}. < < <---===


Then find the length of the third side using  the cosine law.


Then find the perimeter,
</pre>

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By the way, &nbsp;since &nbsp;{{{cos(alpha)}}} &nbsp;may have &nbsp;(and factually has (!)) &nbsp;TWO values at given &nbsp;{{{sin(alpha)}}}, &nbsp;you will have 
TWO possible values for the third side, &nbsp;and, &nbsp;correspondingly, &nbsp;TWO values for the possible perimeter.


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Regrading the solution by the tutor &nbsp;@Mathlover1, &nbsp;keep in mind that she loss one possible answer and makes 
a lot of unnecessary calculations on her way &nbsp;(like finding &nbsp;{{{alpha}}}&nbsp;).