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 : 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: $48$

Question : From the top of a lighthouse at a height of 20 metres above sea-level, the angle of depression of a ship is 30°. The distance of the ship from the foot of the lighthouse is:

Option 1: $20$ m

Option 2: $20 {\sqrt3}$ m

Option 3: $30$ m

Option 4: $30 {\sqrt3}$ m

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:

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

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

Option 3: $\frac{\sqrt{3}}{4}$

Option 4: $\sqrt{3}$

Question : The angles of elevation of a pole from two points which are 75 m and 48 m away from its base are $\alpha$ and $\beta$, respectively. If $\alpha$ and $\beta$ are complementary, then the height of the tower is:

Option 1: 54.5 m

Option 2: 61.5 m

Option 3: 60 m

Option 4: 50 m