Question

Find x rounded to one decimal place.

Answer 1

Check the picture below.

`y√(3)=85\implies y=\cfrac{85}{√(3)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the same 30-60-90 rule for the larger triangle}}{x+y~~ = ~~85√(3)}\implies x+\cfrac{85}{√(3)}=85√(3) \\\\\\ x=85√(3)-\cfrac{85}{√(3)}\implies x=\cfrac{85(3)-85}{√(3)}\implies x=\cfrac{255-85}{√(3)} \\\\\\ x=\cfrac{170}{√(3)}\implies \boxed{x\approx 98.1}`