Find Height of Buildings

[nycmathguy]

 

[MathLover1]

1
first use small triangle and mark base with d
use tan(37) and express d in terms of x and tan(37)

tan(37) =x/d

d=x/tan(37)

then the greater triangle have a base 80+x/tan(37)

so,
tan(18) =x/(80+x/tan(37) )
tan(18)*(80+x/tan(37) ) =x
80tan(18)+x(tan(18)/tan(37) ) =x
25.994+0.4x =x
25.994=x-0.4x
25.994=0.6x
x=25.994/0.6
x=43.3ft

2. follow 1. and do it same way

 

[nycmathguy]

1
first use small triangle and mark base with d
use tan(37) and express d in terms of x and tan(37)

tan(37) =x/d

d=x/tan(37)

then the greater triangle have a base 80+x/tan(37)

so,
tan(18) =x/(80+x/tan(37) )
tan(18)*(80+x/tan(37) ) =x
80tan(18)+x(tan(18)/tan(37) ) =x
25.994+0.4x =x
25.994=x-0.4x
25.994=0.6x
x=25.994/0.6
x=43.3ft

2. follow 1. and do it same way

Not too bad at all. I will tackle 2 this weekend. Yes, I will also squeeze calculus into Saturday and Sunday after the beach.