Question : If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is:
Option 1: $20(\sqrt{3}-1)$ m
Option 2: $20(\sqrt{3}+1)$ m
Option 3: $10(\sqrt{3}-1)$ m
Option 4: $10(\sqrt{3}+1)$ m
Correct Answer: $10(\sqrt{3}+1)$ m
Solution :
In $\Delta$ ABC
$\tan 45°=\frac{AB}{BC}$
⇒ $1=\frac{h}{BC}$
⇒ $BC=h=AB$
In $\Delta$ ABD
$\tan 30°=\frac{AB}{BD}$
⇒ $\frac{1}{\sqrt3}=\frac{h}{h+20}$
⇒ $h+20=h\sqrt{3}$
⇒ $h=\frac{20}{\sqrt{3}–1}$
⇒ $h=\frac{20}{\sqrt{3}–1}×\frac{\sqrt{3+1}}{\sqrt{3+1}}$
⇒ $h=10(\sqrt{3}+1)$ m
Hence, the correct answer is $10(\sqrt{3}+1)$ m.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
