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Introduction to Trigonometry and Its Applications
NCERT Exemplar
CBSE
Grade 10

Question:

If a ladder $15\text{ m}$ long just reaches the top of a vertical wall, and the ladder makes an angle of $60^\circ$ with the wall, then the height of the wall is:
(a) $7.5\text{ m}$
(b) $15\sqrt{3}\text{ m}$
(c) $\dfrac{15\sqrt{3}}{2}\text{ m}$
(d) $15\text{ m}$

Step-by-Step Solution

Key Concept: The angle with the wall is $60^\circ$, so the angle with the ground is $30^\circ$. $\sin 30^\circ = \dfrac{h}{15}$.
Angle with ground $= 90^\circ - 60^\circ = 30^\circ$. [0.5 Mark]
$\sin 30^\circ = \dfrac{h}{15} \Rightarrow \dfrac{1}{2} = \dfrac{h}{15} \Rightarrow h = 7.5\text{ m}$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Finding angle with ground $= 30^\circ$: 0.5 Mark
Applying $\sin 30^\circ = h/15 \Rightarrow h = 7.5\text{ m}$: 0.5 Mark

Correct Answer: $7.5\text{ m}$
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