I don't suggest you taking the significant figures in your working step.ALL the estimation should be taken place after you get the answer
1. h/tan40°=100-h/tan30°
h/tan40°+ h/tan30° =100
h(1/tan40°+ 1/tan30°) =100
h=100/(1/tan40°+ 1/tan30°)
h=34.2(correct to 3 sig,fig,)