Question : A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is $60°$. But the angle of elevation is $30°$ from a point which is at a distance $20\sqrt{3}$ ft away from the bank. Then the height of the tree is:
Option 1: 60 ft
Option 2: 45 ft
Option 3: 30 ft
Option 4: 15 ft
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: 30 ft
Solution :
Let $h$ be the height of the tree and $x$ be the breadth of the river.
From the above figure we get,
$\tan60°=\frac{h}{x}$
⇒ $\sqrt{3}=\frac{h}{x}$
⇒ $x=\frac{h}{\sqrt{3}}$----------(equation 1)
Also, $\tan30°=\frac{h}{x+20\sqrt{3}}$
⇒ $\frac{1}{\sqrt{3}}=\frac{h}{x+20\sqrt{3}}$
⇒ $x=h\sqrt{3}–20\sqrt{3}$ ---------(equation 2)
Now equalising the values of $x$ from both equations we get,
⇒ $h\sqrt{3}–20\sqrt{3}=\frac{h}{\sqrt{3}}$
⇒ $3h–60=h$ ⇒ $2h=60$ ⇒ $h=30$ ft
Hence, the correct answer is 30 ft.
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 “”.
