Question 975346
Pick either end of the base for dealing with the angle there, and maybe use Law of Cosines.  Choosing the sides 13 and 14,
{{{13^2+14^2-2*13*14*cos(x)=15^2}}}


{{{13^2+14^2-15^2=2*13*14*cos(x)}}}
{{{cos(x)=(13^2+14^2-15^2)/(2*13*14)}}}.


What you want is height, which is {{{highlight(13*sin(x))}}}.  Compute cosine, and use the identify  {{{sin^2(x)+cos^2(x)=1}}}  to find sin(x).  You should be able to finish this.



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{{{cos(x)=5/13}}}.
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{{{sin^2(x)=1^2-(5/13)^2}}}
{{{sin^2(x)=(169-25)/169}}}
{{{sin^2(x)=144/169}}}
{{{sin(x)=12/13}}}
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Height is  {{{13(12/13)=highlight(12)}}}.