Quantitative Aptitude Ques 1034
Question: From the top of a tree of height $ 120m, $ the angle of depression of two boats in the same line with the foot of the tree and on the same side of it are $ 45{}^\circ $ and $ 60{}^\circ , $ respectively. The distance between the boats is
Options:
A) $ 40(3-\sqrt{3})m $
B) $ 40(3\sqrt{3}-1)m $
C) $ 120(\sqrt{3}-1)m $
D) $ 12(3-\sqrt{3})m $
Show Answer
Answer:
Correct Answer: A
Solution:
- Given, height of the tree $ =120m $
In the given figure two depression angles $ 45{}^\circ $ and $ 60{}^\circ $ are given,
Now, $ \angle CAO=\angle ACB=60{}^\circ $ [alternate angles]
Similarly, $ \angle DAO=\angle ADB $
In $ \Delta ADB, $ $ \tan 45{}^\circ =\frac{AB}{BD} $
$ \Rightarrow $ $ 1=\frac{120}{BD} $
$ \Rightarrow $ $ BD=120m $
In $ \Delta ACB, $ $ \tan 60{}^\circ =\frac{AB}{BC} $
$ \Rightarrow $ $ \sqrt{3}=\frac{120}{BC} $
$ \Rightarrow $ $ BC=\frac{120}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=40\sqrt{3}m $ Thus, distance between both the boats, $ CD=BD-BC $ $ =120-40\sqrt{3}=40(3-\sqrt{3})m $
BETA
