Question

if two towers of height x and y subtend angles of 45 degree and 60 degree respectively at the centre of a line joining their feet then find the ratio of (x+y)and y

Answer 1

Thus, The ratio of $\frac{(x+y)}{y}$ is $\frac{1+\sqrt{3} }{\sqrt{3} }$

Step-by-step explanation:

Given,

Two towers of height $x$ and $y$ subtend angles of $45$° and $60$° then

Find the ratio of $\frac{(x+y)}{y} =?$

From figure,

  $tan45=\frac{x}{AO}$

⇒$x=AO.tan45$

And,

  $tan60=\frac{y}{BO}$

⇒$y=BO.tan60$

∴ $(x+y)=AO.tan45+BO.tan60$

              $=BO(tan45+tan60)$  (∵$AO=BO$ )

∴ $\frac{(x+y)}{y} =\frac{BO(tan45+tan60)}{BO.tan60}$

           $=1+\frac{tan45}{tan60}$

           $=1+\frac{1}{\sqrt{3} }$

           $=\frac{1+\sqrt{3} }{\sqrt{3} }$

∴ The ratio of $\frac{(x+y)}{y}$ is $\frac{1+\sqrt{3} }{\sqrt{3} }$

Answer 2

Step-by-step explanation:

i guess it will be helpful

glad to help