Question : A man on the top of a tower, standing on the seashore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30° to 60°. How soon does the boat reach the seashore?
Option 1: 5 minutes
Option 2: 7 minutes
Option 3: 10 minutes
Option 4: 15 minutes
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: 5 minutes
Solution :
Given: The boat takes 10 minutes for the angle of depression to change from 30° to 60°.
We know the trigonometric ratio, $\tan\theta=\frac{\text{Height}}{\text{Base}}$.
In $\triangle ABC$, $\tan \ 30° =\frac{AB}{BC}$
$⇒\frac{1}{\sqrt3} = \frac{AB}{BC}$
$⇒AB=\frac{BC}{\sqrt3}$-------(equation 1)
In $\triangle ABD$, $\tan \ 60° =\frac{AB}{BD}$
$⇒\sqrt3 = \frac{AB}{BD}$
$⇒AB = \sqrt3 BD$------(equation 2)
From equation 1 and equation 2, we get,
$⇒\frac{BC}{\sqrt3}=\sqrt3 BD$
$⇒BC= 3 BD$
Also, $BC= BD+CD$
$⇒3BD=BD+10x$ [Here $CD= 10x$, if the speed of boat is $x$ m/minute]
$⇒2BD=10x$
$⇒BD=5x$
So, Time taken = $\frac{5x}{x}$ = 5 minutes
Hence, the correct answer is 5 minutes.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CGL
