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Mathematics · 2023 · 5 marks
CBSE 2023 · Region 5 · Set 3 · Q35
Two pillars are standing on either side of a $\displaystyle 80$ m wide road. Height of one pillar is $\displaystyle 20$ m more than the height of the other pillar. From a point on the road between the pillars, the angle of elevation of the higher pillar is $\displaystyle 60$°, whereas that of the other pillar is $\displaystyle 30$°. Find the position of the point between the pillars and the height of each pillar. (Use $\displaystyle \sqrt{3}=1 \cdot 73$ )
Marking-scheme solution
Let PQ and RS be the pillars.
\[\tan 60^{\circ}=\sqrt{3}=\frac{h+20}{x} \Rightarrow h+20=x \sqrt{3}
\]
\[\tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{h}{80-\mathrm{x}} \Rightarrow h \sqrt{3}=80-\mathrm{x}
\]
Using (i) and (ii) $\displaystyle \mathrm{x}=28 \cdot 65, \mathrm{~h}=29 \cdot 56$
\[\begin{array}{l}
\mathrm{AP}=28 \cdot 65 \mathrm{~m}, \mathrm{AR}=51 \cdot 35 \mathrm{~m} \\
\mathrm{PQ}=\mathrm{h}+20=49.56 \mathrm{~m} \text { and } \mathrm{RS}=29.56 \mathrm{~m}
\end{array}
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CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.