Question 918778


let's a height of the pole be {{{h[1]}} casts a shadow  {{{Sh[1]}}}

and a height of the tower {{{h[2]}} casts a shadow  {{{Sh[2]}}}
 
given:

the pole:{{{h[1]=2.7m}}} and casts a shadow that is {{{Sh[1]=11.1m}}} 

the tower: casts a shadow that is {{{Sh[2]=45.25m}}} 

find: {{{h[2]}} or how tall is the tower 

we know that both pole and tower, their shadows, and ground form a right angle triangle and these are similar

we know that corresponding sides of similar triangles are proportional

so, {{{h[1]:h[2]=Sh[1]:Sh[2]}}} ...plug in given values


{{{2.7m:h[2]=11.1m:45.25m}}} ...solve for {{{h[2]}}


{{{h[2]*11.1m=2.7m*45.25m}}}

{{{h[2]*11.1m=122.175m^2}}}

{{{h[2]=122.175m^cross(2)/11.1cross(m)}}}

{{{h[2]=122.175m/11.1}}}

{{{h[2]=11.00675675675676m}}}

{{{h[2]=11.01m}}}