Introduction to Trigonometry and Its Applications
NCERT Exemplar Ch 08
CBSE_NCERT_EXEMPLAR_CH08
Grade 10
Question:
If the angle of elevation of the sun is $60^\circ$, then the length of the shadow cast by a tree of height $h$ metres is:
$\dfrac{h}{\sqrt{3}}\text{ m}$
$h\sqrt{3}\text{ m}$
$\dfrac{h}{2}\text{ m}$
$\dfrac{h}{\sqrt{2}}\text{ m}$
Step-by-Step Solution
Key Concept: $\tan 60^\circ = \dfrac{\text{Height}}{\text{Shadow}} = \dfrac{h}{x}$.
Stepwise Solution:
$\sqrt{3} = \dfrac{h}{x} \Rightarrow x = \dfrac{h}{\sqrt{3}}\text{ m}$. [1.0 Mark]
Marking Scheme:
• Applying $\tan 60^\circ = h/x \Rightarrow x = h/\sqrt{3}$: 1.0 Mark
Correct Answer: $\dfrac{h}{\sqrt{3}}\text{ m}$
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