71). The elevation of the top of a tower from a point on the ground is 45°. On travelling 60 m from the point towards the tower the elevation of the top becomes 60°. The height of the tower (in metres) is
| A). \( \Large 30 \) |
| B). \( \Large 30(3-\sqrt{3}) \) |
| C). \( \Large 30(3+\sqrt{3}) \) |
| D). \( \Large 30\sqrt{3} \) |
|
72). The top of two poles of height 24m and 36m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is
| A). \( \Large 6m \) |
| B). \( \Large 8\sqrt{3}m \) |
| C). \( \Large 8m \) |
| D). \( \Large 6\sqrt{3}m \) |
|
73). From the top of a hill 200m high the angle of depression of the top and the bottom of a tower are observed to be 30° and 60°. The height of the tower is (in m) ;
| A). \( \Large \frac{400\sqrt{3}}{3} \) |
| B). \( \Large 166\frac{2}{3} \) |
| C). \( \Large 133\frac{1}{3} \) |
| D). \( \Large 200\sqrt{3} \) |
|
74). From a tower 125 metres high the angle of depression of two objects, which are in horizontal line through the base of the tower are 45° and 30° and they are on the same side of the tower. The distance (in metres) between the objects is
| A). \( \Large 125\sqrt{3} \) |
| B). \( \Large 125(\sqrt{3}-1) \) |
| C). \( \Large 125/(\sqrt{3}-1) \) |
| D). \( \Large 125(\sqrt{3}+1) \) |
|
75). From a point P on the ground the angle of elevation of the top of a 10m tall building is 30° A flag is hoisted at the top of var building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff (Take \( \sqrt{3}=1.732 \))
| A). \( \Large 10(\sqrt{3}+2)m \) |
| B). \( \Large 10(\sqrt{30}+1)m \) |
| C). \( \Large 10\sqrt{3}m \) |
| D). \( \Large 7.32m \) |
|
76). From a point 20 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The height of the tower is
| A). \( \Large 10\sqrt{3}m \) |
| B). \( \Large 20\sqrt{3}m \) |
| C). \( \Large \frac{10}{\sqrt{3}}m \) |
| D). \( \Large \frac{20}{\sqrt{3}}m \) |
|
77). The angle of elevation of ladder leaning against a house is 60° and the foot of the ladder is 6.5 metres from the house. The length of the ladder is
| A). \( \frac{13}{\sqrt{3}} \) |
| B). 13 meters |
| C). 15 meters |
| D). 3.25 metres |
|
78). The angle of elevation of sun changes from 30° to 45°, the length of the shadow of a pole. decreases by 4 metres, the height of the pole is (Assume \(\sqrt{3}=1.732 \))
| A). 1.464m |
| B). 9.464m |
| C). 3.648m |
| D). 5.464 m |
|
79). A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 10 metres. From the top of the pole the angle of elevation of the top of the tower and angle of depression of the foot 0f the towervare 60° and 30° respectively. The height of the tower is
| A). 20 m |
| B). 30 m |
| C). 40 m |
| D). 50 m |
|
80). A 1.6 m tall observer is 45 metres away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower in metres is (Take \( \sqrt{3} \) =1.732)
| A). 25.98 |
| B). 26.58 |
| C). 27.58 |
| D). 27.98 |
|
