Question 1044038

let the horizontal distance from the balconies be {{{y}}}
if the height to  the 1st balcony is {{{x}}},  than the height to  the  2nd balcony is {{{x+6.3}}}

 if the angle of elevation to the first balcony is {{{19}}} degrees, you use right angle triangle whose legs are {{{x}}} and {{{y}}}, and we will have

{{{tan(19)=x/y}}}

=> {{{y=x/tan(19)}}}

 the second balcony, 6.3 meters directly above the first, is 29 degrees, so we have

{{{tan(29)=(x+6.3)/y}}}

=> {{{y=(x+6.3)/tan(29)}}}

since {{{y}}} same in both cases, we have:

{{{x/tan(19)=(x+6.3)/tan(29)}}}

{{{x/0.34432761=(x+6.3)/0.5543}}}...........cross multiply

{{{0.5543x=0.34432761(x+6.3)}}}

{{{0.5543x=0.34432761x+2.169263943}}}

{{{0.5543x-0.34432761x=2.169263943}}}

{{{0.209972 x=2.169263943}}}

{{{x=2.169263943/0.209972}}} 

{{{x=10.3312057941}}}...round it

{{{x=10.3}}}

 
so, your answer is: b. {{{10.3}}} meters