Question : The angle of elevation of an aeroplane as observed from a point 30 metres above the transparent water surface of a lake is 30° and the angle of the depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water surface of the lake is:
Option 1: 60 metres
Option 2: 45 metres
Option 3: 50 metres
Option 4: 75 metres
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 60 metres
Solution : AB = transparent water surface then according to question, $\triangle$CPM = 30°; $\angle$C'PM = 60° CM = $h$ CB = Height of the aeroplane from the water surface of the lake = $h + 30$ $\therefore$ C'B = $h + 30$ In $\triangle$CMP, tan 30° = $\frac{CM}{PM}$ $⇒\frac{1}{\sqrt{3}} = \frac{h}{PM}$ $\therefore$ PM = ${\sqrt{3}}$h------------(1) In $\triangle$PMC', tan 60° = $\frac{C'M}{PM}$ $⇒{\sqrt{3}} = \frac{h+30+30}{PM}$ $\therefore$ PM = $\frac{h+60}{\sqrt{3}}$-----------(2) From equation 1 and 2, we get, $3h = h+60$ $⇒ h = 30 $ $\therefore$ CB = BM + CM = 30 + 30 = 60 metres Hence, the correct answer is 60 metres.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : The angle of elevation of an aeroplane from a point on the ground is 60°. After flying for 30 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 4500 metres, then what is the speed (in m/s) of an aeroplane?
Question : From the top of a 20 metres high building, the angle of elevation from the top of a tower is 60° and the angle of depression of its foot is at 45°, then the height of the tower is: $(\sqrt{3} = 1.732)$
Question : The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar raised so that its angle of elevation at the same point may be 45°, is:
Question : The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/h is:
Question : If the angle of elevation of the top of a pillar from the ground level is raised from 30° to 60°, the length of the shadow of a pillar of height $50\sqrt{3}$ metres will be decreased by:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile