Question : Two posts are 2 metres apart. Both posts are on the same side of a tree. If the angles of depressions of these posts when observed from the top of the tree are 45° and 60° respectively, then the height of the tree is:
Option 1: $(3-\sqrt{3})$ metres
Option 2: $(3+\sqrt{3})$ metres
Option 3: $(-3+\sqrt{3})$ metres
Option 4: $(3-\sqrt{2})$ metres
Correct Answer: $(3+\sqrt{3})$ metres
Solution : CD = 2 metres BD = $x$ metre AB = Tree = $h$ metre From ∆ ABC, tan 45° = $\frac{AB}{BC}$ ⇒ $1 = \frac{h}{x+2}$ $\therefore h = (x + 2)$ metre .....(i) From ∆ ABD, $\tan 60° = \frac{AB}{BD}$ ⇒ $\sqrt{3} = \frac{h}{x}$ $\therefore x = \frac{h}{\sqrt{3}}$ metre .....(ii) Putting the value of $x$ in equation (i), we get $h=\frac{h}{\sqrt{3}}+2$ ⇒ $h(\frac{\sqrt{3}-1}{\sqrt{3}})=2$ ⇒ $h= \frac{2\sqrt{3}}{\sqrt{3}-1}$ ⇒ $h= \frac{2\sqrt{3}(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}$ $\therefore h=\frac{6+2\sqrt{3}}{2}=(3+\sqrt{3})$ metres So, the height of the tree is $(3+\sqrt{3})$ metres. Hence, the correct answer is $(3+\sqrt{3})$ metres.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : The cliff of a mountain is 180 m high and the angles of depression of two ships on either side of the cliff are 30° and 60°. What is the distance between the two ships?
Question : The shadow of a tower standing on a level plane is 40 metres longer when the sun's altitude is 45°, than when it is 60°. The height of the tower is:
Question : If the height of a pole is $2\sqrt{3}$ metres and the length of its shadow is 2 metres, then the angle of elevation of the sun is:
Question : The two banks of a canal are straight and parallel. A, B, and C are three persons, of whom A stands on one bank and B and C on the opposite banks. B finds the angle ABC is 30°, while C finds that the angle ACB is 60°. If B and C are 100 metres apart, the breadth of the
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:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile