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Some Applications of Trigonometry
CH09 Question Bank
CBSE_CH09_QUESTION_BANK
Grade 10

Question:

Two poles of heights $6$ m and $11$ m stand vertically on a level ground. The angle of elevation of the top of the taller pole, as observed from the top of the shorter pole, is $30^\circ$. Find the distance between the two poles.

Step-by-Step Solution

Key Concept: Draw a horizontal line from the top of the shorter pole to the taller pole; the vertical rise (height difference) and the horizontal distance between the poles form a single right triangle with the given angle.
Height difference between the poles $=11-6=5$ m. [1.5 Marks]

Drawing a horizontal line from the top of the shorter pole, a right triangle is formed with the vertical leg $=5$ m (height difference) and the horizontal leg $=$ the distance between the poles, $d$. [1.5 Marks]

$\tan30^\circ=\dfrac{5}{d}\Rightarrow\dfrac{1}{\sqrt3}=\dfrac{5}{d}$. [1.0 Mark]

$d=5\sqrt3$ m $\approx8.66$ m. [1.0 Mark]

Correct Answer:
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