MCQ
A lamp post $5 \sqrt{3} m$ high casts a shadow $5 m$ long on the ground. The Sun's elevation at this moment is
- A$30^{\circ}$
- B$45^{\circ}$
- ✓$60^{\circ}$
- D$90^{\circ}$
✓
Answer
Correct option: C.
$60^{\circ}$
(c) : Let $A B$ be the lamp post and $B C$ be the shadow of it. Let Sun's elevation be $\theta$.
In $\triangle A B C$,
$
\tan \theta=\frac{A B}{B C}=\frac{5 \sqrt{3}}{5}=\sqrt{3}
$
$\Rightarrow \tan \theta=\tan 60^{\circ}$$
\Rightarrow \theta=60^{\circ}
$
Hence, Sun's elevation at the moment is $60^{\circ}$.
In $\triangle A B C$,
$
\tan \theta=\frac{A B}{B C}=\frac{5 \sqrt{3}}{5}=\sqrt{3}
$
$\Rightarrow \tan \theta=\tan 60^{\circ}$$
\Rightarrow \theta=60^{\circ}
$
Hence, Sun's elevation at the moment is $60^{\circ}$.
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