Use the fact that tana=h/(y-x) and tan b=h/y to show that h = (xtanatanb)/(tana-tanb)

Question

Use the fact that tana=h/(y-x) and tan b=h/y to show that h = (xtanatanb)/(tana-tanb)

Answer 1

tana = h/(y-x) and tanb = h/y

So, x(tana)(tanb) = x[h/(y-x)][h/y] = xh² / [y(y-x)]

and tana - tanb = h/(y-x) - h/y = [hy - h(y-x)] / [y(y-x)] = hx / [y(y-x)]

Therefore, (xtanatanb) / (tana - tanb) = [xh² / (y(y-x))] ÷ [hx / (y(y-x))]

= [xh² / (y(y-x))] [ (y(y-x)) / (hx)] = xh² / (hx) = h