1 View

Question : Two posts are 2 metres apart. Both posts are on the same side of a tree. If the angles of depressions of these posts when observed from the top of the tree are 45° and 60° respectively, then the height of the tree is:

Option 1: $(3-\sqrt{3})$ metres

Option 2: $(3+\sqrt{3})$ metres

Option 3: $(-3+\sqrt{3})$ metres

Option 4: $(3-\sqrt{2})$ metres


Team Careers360 22nd Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: $(3+\sqrt{3})$ metres


Solution :
CD = 2 metres
BD = $x$ metre
AB = Tree = $h$ metre
From ∆ ABC,
tan 45° = $\frac{AB}{BC}$
⇒ $1 = \frac{h}{x+2}$
$\therefore h = (x + 2)$ metre .....(i)
From ∆ ABD,
$\tan 60° = \frac{AB}{BD}$
⇒ $\sqrt{3} = \frac{h}{x}$
$\therefore x = \frac{h}{\sqrt{3}}$ metre .....(ii)
Putting the value of $x$ in equation (i), we get
$h=\frac{h}{\sqrt{3}}+2$
⇒ $h(\frac{\sqrt{3}-1}{\sqrt{3}})=2$
⇒ $h= \frac{2\sqrt{3}}{\sqrt{3}-1}$
⇒ $h= \frac{2\sqrt{3}(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}$
$\therefore h=\frac{6+2\sqrt{3}}{2}=(3+\sqrt{3})$ metres
So, the height of the tree is $(3+\sqrt{3})$ metres.
Hence, the correct answer is $(3+\sqrt{3})$ metres.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books