Question

The tops of two towers of height x and y , standing on level ground , subtend angles of 30 and 60 respectively at the centre of the line joining their feet, then find x/y.

Answer 1

Answer:1/3

Step-by-step explanation:tan30=x/BE

1/

Answer 2

Suppose E is the centre of the line joining the feet of the two towers i.e. BD

Now , in triangle ABE

$\sf{{\dfrac{AB}{BE}}=tan30°}$

➝ $\sf{{\dfrac{x}{BE}}={\sqrt{3}}}$

➝ $\sf{{BE}={\sqrt{3x}}}$ ___ (1)

Also ,

In triangle CDE

$\sf{{\dfrac{CD}{DE}}=tan60°}$

➝ DE = ${\sf{\dfrac{y}{\sqrt{3}}}}$ ___ (2)

Now BE = DE ___ (3) [E is mid point of BD]

So , from (1) , (2) and (3) , we get

${\sf {\sqrt{3x}} = {\dfrac{y}{\sqrt{3}}}}$

➝ ${\sf{\dfrac{x}{y}} = {\dfrac {1}{3}}}$

Hence , the ratio of x and y is 1:3