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

Question : An aeroplane flying horizontally at a height of 3 km above the ground is observed at a certain point on earth to subtend an angle of $60^\circ$. After 15 seconds of flight, its angle of elevation is changed to $30^\circ$. The speed of the aeroplane (Take $\sqrt{3}=1.732$) is:

Option 1: 230.63 m/s

Option 2: 230.93 m/s

Option 3: 235.85 m/s

Option 4: 236.25 m/s

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?

Option 1: $50\sqrt3$

Option 2: $100\sqrt3$

Option 3: $200\sqrt3$

Option 4: $300\sqrt3$

Question : A tower is broken at a point P above the ground. The top of the tower makes an angle of $60^\circ$ with the ground at Q. From another point R on the opposite side Q angle of elevation of point P is $30^\circ$. If QR = 180 m, what is the total height (in meters) of the tower?

Option 1: $90$

Option 2: $45\sqrt{3}$

Option 3: $45(\sqrt{3}+1)$

Option 4: $45(\sqrt{3}+2)$

Question : $D$ is a point on the side $BC$ of a triangle $ABC$ such that $AD\perp BC$. $E$ is a point on $AD$ for which $AE:ED=5:1$. If $\angle BAD=30^{\circ}$ and $\tan \left ( \angle ACB \right )=6\tan \left ( \angle DBE \right )$, then $\angle ACB =$

Option 1: $30^{\circ}$

Option 2: $45^{\circ}$

Option 3: $60^{\circ}$

Option 4: $15^{\circ}$