Question

∆ABC abd ∆DEF are righted angled triangles if ∆ABC sino=3/5 and∆DEF tano=9/12 then find the ratio of ∆ABC and. ∆ DEF

Answer 1

we know
sinx=perpendicular/hypotenus
3/5=perpendicular/hypotenus
hence triangle ABC have 3,4,5 sides in which 3 is perpendicular ,4 is base and 5 is hypotenus.
in the same way
tanx=perpendicular/base
9/12 =perpendicular/base
hence triangle DEF perpendicular is 9 , base is 12 and hypotenus is 15
now
ar (ABC)/ar(DEF)=(1/2 x 3 x 4 )/(1/2 x 9 x 12)=1/9
triangle ABC=1/9 triangle DEF