18 Views

Question : Two ships are on the opposite of a lighthouse such that all three of them are collinear. The angles of depression of the two ships from the top of the lighthouse are 30° and 60°. If the ships are $230 \sqrt{3}$ m apart, then find the height of the lighthouse (in m).

Option 1: 175.4

Option 2: 165.2

Option 3: 172.5

Option 4: 180.5


Team Careers360 8th Jan, 2024
Answer (1)
Team Careers360 10th Jan, 2024

Correct Answer: 172.5


Solution :
Given: The distance between the ships is BC = $230\sqrt3$ m
Let the height of the lighthouse AD be $h$ m.
From $\triangle$ABD we get,
$\tan30°=\frac{AD}{BD}$ ⇒ BD = $h\sqrt3$
Again from $\triangle$ACD we get,
$\tan60°=\frac{AD}{CD}$ ⇒ CD = $\frac{h}{\sqrt3}$
According to the question,
$h\sqrt3+\frac{h}{\sqrt3}=230\sqrt3$
⇒ $3h+h=690$
⇒ $4h=690$
⇒ $h=\frac{690}{4}=172.5$ m
Hence, the correct answer is 172.5 m.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

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
GRE ® Registrations 2024
Apply
Apply for GRE® Test now & save 10% with ApplyShop Gift Card | World's most used Admission Test for Graduate & Professional Schools
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