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Some Applications of Trigonometry
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10

Question:

[Section A]

The shadow of a tower standing on level ground is $40$ m longer when the sun's altitude is $30^\circ$ than when it is $60^\circ$. The height of the tower is:

(a) $20$ m
(b) $20\sqrt3$ m
(c) $40$ m
(d) $40\sqrt3$ m

Step-by-Step Solution

Key Concept: $h = \dfrac{40}{\cot30^\circ - \cot60^\circ} = \dfrac{40}{\sqrt3 - 1/\sqrt3} = 20\sqrt3$ m.
$h(\sqrt3 - 1/\sqrt3) = 40 \Rightarrow h(2/\sqrt3) = 40 \Rightarrow h = 20\sqrt3$ m. [1.0 Mark]

Correct Answer: (b) 20√3 m (or 40 m depending on options list)
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