Question : If the angle of elevation of a balloon from two consecutive kilometre stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be:
Option 1: $\frac{\sqrt{3}}{2}$ km
Option 2: $\frac{1}{2}$ km
Option 3: $\frac{2}{\sqrt{3}}$ km
Option 4: $3\sqrt{3}$ km
Correct Answer: $\frac{\sqrt{3}}{2}$ km
Solution : Let the height of the balloon be $h$. $\tan60°=\frac{h}{x}$ ⇒ $\sqrt{3}=\frac{h}{x}$ ⇒ $x=\frac{h}{\sqrt{3}}$ ------(1) $\tan30°=\frac{h}{x+1}$ ⇒ $\frac{1}{\sqrt{3}}=\frac{h}{\frac{h}{\sqrt{3}}+1}$ ⇒ $\frac{1}{\sqrt{3}}=\frac{\sqrt{3}h}{h+\sqrt{3}}$ ⇒ $3h=h+\sqrt{3}$ ⇒ $2h=\sqrt{3}$ ⇒ $h=\frac{\sqrt{3}}{2}$ km Hence, the correct answer is $\frac{\sqrt{3}}{2}$ km.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
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:
Question : A pole of length 7 m is fixed vertically on the top of a tower. The angle of elevation of the top of the pole observed from a point on the ground is 60° and the angle of depression of the same point on the ground from the top of the tower is 45°. The height (in m) of
Question : If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar 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 : From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile