Question

The two towers of height x and y. Standing on level ground, subtend angles of 30° and
60° respectively at the center of the line joining their feet. Then find x:y.
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Answer 1

$\huge\underline\mathfrak\red{Question }$

The two towers of height x and y. Standing on level ground, subtend angles of 30° and 60° respectively at the center of the line joining their feet.

Then find x : y.

★ solution :

In ᐃ ABC

$\tan(30) = \frac{x}{p}$

↪x = p tan 30° .....(1)

now in ᐃDEC

$tan(60) = \frac{y}{p}$

↪y = p tan 60° .....(2)

↪ divide equation 1 and 2

then

$\frac{x}{y} = \frac{ \tan(30) }{ \tan(60) }$

$\frac{x}{y } = \frac{ \frac{1}{ \sqrt{3} } }{ \sqrt{3} }$

$\frac{x}{y} = \frac{1}{3}$

↪ therefore ; x : y = 1:3