Question 1196263
Draw the described situation.
T, point at tip of the hut.

Understand, a point is directly under T and is on segment BA.
Triangle BTA;
Interior angle at B is 45 degrees and interior angle at A is 55 degrees.
x, the length from B to the point on the segment, underneath T.
15-x, the length from A to the point on the segment, underneath T.


How high the tip of the the hunt,  y.


Check the triangle part with the 45 elevation angle.  That part is special 45-45-90 triangle.  this mean,  {{{y=x}}}.


{{{system(x/x=1=tan(45),y/(15-y)=tan(55))}}}


Just solving the second equation,


{{{y=(15*tan(55))/(1+tan(55))}}}