Some Applications of Trigonometry Question - CBSE_CH09_QUESTION_BANK

Question

Two poles of equal height stand on either side of a road $80$ m wide. From a point on the road between the poles, the angles of elevation of the top of the poles are $30^\circ$ and $60^\circ$. Find the height of the poles and the distance of the point from each pole. (Assume the point is directly between the two poles, on the line joining their bases.)

Accepted Answer

Let the height of each pole be $h$, and let the point be at distance $x$ from the pole with elevation $60^\circ$, so it is at distance $(80-x)$ from the pole with elevation $30^\circ$. [0.5 Mark]

$ an60^\circ=\dfrac{h}{x}\Rightarrow h=x\sqrt3$ — (1). $ an30^\circ=\dfrac{h}{80-x}\Rightarrow h=\dfrac{80-x}{\sqrt3}$ — (2). [1.0 Mark]

Equating (1) and (2): $x\sqrt3=\dfrac{80-x}{\sqrt3}\Rightarrow 3x=80-x\Rightarrow 4x=80\Rightarrow x=20$ m. [1.0 Mark]

$h=20\sqrt3$ m; the point is $20$ m from one pole and $60$ m from the other. [0.5 Mark]

Question:

Step-by-Step Solution

Master Some Applications of Trigonometry with Mathbee