Question

The tops of two tower of height x&y standing on level ground sudtend angles of 30°and 60°resp at the centre of the line joining their feet then find x ratio y

Answer 1

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Answer 2

Answer:

Ratio of x to y is 1 : 3.

Step-by-step explanation:

Given: Height of two towers is x & y

           Angle subtended at center of line joining their feet are 30° and 60°

To find: ratio x to y

Given Angles are Angle of depression but we know angle of depression is equal to angle of elevation.

Thus, use give angles at angle of elevation.

Also, Angle made at center of line joining there feet .i.e., C is mid point and BC = CE.

In Δ ABC

using trigonometric ratio

$tan\,30^{\circ}=\frac{AB}{BC}$

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

$BC=x\times\sqrt{3}$

$x=\frac{BC}{\sqrt{3}}$

In Δ CDE

using trigonometric ratio,

$tan\,60^{\circ}=\frac{DE}{CE}$

$\sqrt{3}=\frac{y}{CE}$

$CE= \frac{y}{\sqrt{3}}$

$y=CE\times\sqrt{3}$

Now,

$\frac{x}{y}=\frac{\frac{BC}{\sqrt{3}}}{CE\times\sqrt{3}}$

$\frac{x}{y}=\frac{BC}{CE\times\sqrt{3}\times\sqrt{3}}$

$\frac{x}{y}=\frac{BC}{CE\times3}$

$\frac{x}{y}=\frac{BC}{BC\times3}$      ( ∵ BC = CE )

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

Therefore, Ratio of x to y is 1 : 3.