2 Views

Question : From an aeroplane just over a straight road, the angles of depression of two consecutive kilometre stones situated at opposite sides of the aeroplane were found to be 60° and 30°, respectively. The height (in km) of the aeroplane from the road at that instant, is:

Option 1: $\frac{\sqrt{3}}{2}$

Option 2: $\frac{\sqrt{3}}{3}$

Option 3: $\frac{\sqrt{3}}{4}$

Option 4: $\sqrt{3}$


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 15th Jan, 2024

Correct Answer: $\frac{\sqrt{3}}{4}$


Solution :
Let the aeroplane be at point A at a height $h$ above ground level.
Let B and C be two consecutive kilometre stones with angles of depression $60°$ and $30°$, respectively.
Now, $\tan 60°=\frac{h}{BD}$ and $\tan 30°=\frac{h}{CD}$
⇒ $BD=h\cot 60°$ and $CD=h\cot 30°$
$\because BD+CD=1$
$\therefore h\cot 60°+h\cot 30°=1$
⇒ $h(\frac{1}{\sqrt{3}}+\sqrt{3})=1$
⇒ $h=\frac{\sqrt{3}}4$
Hence, the correct answer is $\frac{\sqrt{3}}4$ km.

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