Question : Two points A and B are on the ground and on opposite sides of a tower. A is closer to the foot of the tower by 42 m than B. If the angles of elevation of the top of the tower, as observed from A and B are 60° and 45°, respectively, then the height of the tower is closest to:

Option 1: 87.6 m

Option 2: 98.6 m

Option 3: 88.2 m

Option 4: 99.4 m

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

Question : A 22 m long ladder (whose foot is on the ground) leans against a wall making an angle of 60° with the wall. What is the height (in m) of the point where the ladder touches the wall from the ground?

Option 1: $\frac{22 \sqrt{2}}{3}$

Option 2: $11 \sqrt{2}$

Option 3: $11$

Option 4: $11 \sqrt{3}$

Question : The angle of elevation of an aeroplane from a point on the ground is 60°. After 15 seconds of flight, the elevation changes to 30°. If the aeroplane is flying at a height of $1500\sqrt{3}$ metre, find the speed of the plane:

Option 1: 300 m/sec

Option 2: 200 m/sec

Option 3: 100 m/sec

Option 4: 150 m/sec

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?

Option 1: $48 \sqrt{3}$

Option 2: $36$

Option 3: $36 \sqrt{3}$

Option 4: $48$