Question

prove that the area of any triangle XYZ is y^2*sin(x)*sin(z)/2*sin(y)

Answer 1

Draw the figure.

draw a line from X angle perpendicular to side x.
Note then that zsinY=ysinZ or
z=ysinZ/sinY

now draw a line from angle Y to side y perpendicular to y.
Note that area=1/2 bh=1/2 y*zsinX

then area= 1/2 ysinX*ysinZ/sinY
QED