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Introduction of Trigonometry and its Application — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry and its Application1 Mark
MCQ
Choose the correct answer from the given four options.
A pole 6m high casts a shadow $2\sqrt{3}\text{m}$ long on the ground, then the Sun’s elevation is:
  • ✓
    60º
  • B
    45º
  • C
    30º
  • D
    90º
✓

Answer

Correct option: A.
60º
Let $\text{BC}=6\text{m}$ be the height of the pole and $\text{AB}=2\sqrt{3}\text{m}$ be the lenth of the shadow on the ground. let the Sun's makes an angle $\theta$ on the ground.
$\text{Now, in }\triangle\text{BAC},\ \tan\theta=\frac{\text{BC}}{\text{AB}}$
$\Rightarrow\ \tan\theta=\frac{6}{2\sqrt{3}}=\frac{3}{\sqrt{3}}.\frac{\sqrt{3}}{\sqrt{3}}$
$\Rightarrow\ \tan\theta=\frac{3\sqrt{3}}{3}=\sqrt{3}=\tan60^\circ\ [\because\tan60^\circ=\sqrt{3}]$
$\therefore\ \theta=60^\circ$
Hence, the Sun's elevation is 60°.

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