31). On walking 120 m towards a Chimney in a horizontal line through its base the angle of elevation of tip of the chimney changes from \( \Large 30 ^{\circ} \) to \( \Large 45 ^{\circ} \). The height of the chimney is
| A). 120 m |
| B). \( \Large 60 \left(\sqrt{3} - 1\right) \) m |
| C). \( \Large 60 \left(\sqrt{3} + 1\right) \) m |
| D). None of these |
|
32). A man standing at a point P is watching the top of elevation of \( \Large 30 ^{\circ} \). The man walks some distance towards the tower and then his angle of elevation of the top of the tower is \( \Large 60 ^{\circ} \). If the height of the tower is 30 m, then the distance he moves is
| A). 20 m |
| B). \( \Large 20\sqrt{3} \) m |
| C). 22 m |
| D). \( \Large 22\sqrt{3} \) m |
|
33). The angle of elevation of the top of a tower from the bottom of a building is twice that from its top. What is the height of the building. if the height of the tower is 75 m and the angle of elevation of the top of the tower from the bottom of the building is \( \Large 60 ^{\circ} \)?
| A). 25 m |
| B). 37.5 m |
| C). 50 m |
| D). 60 m |
|
34). The angles of elevation of the top of a tower from two points which are at distances of 10 m and 5 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is
| A). 5 m |
| B). 15 m |
| C). \( \Large \sqrt{50} \) m |
| D). \( \Large \sqrt{75} \) m |
|
35). The angles of elevation of the top of an inaccessible tower from two points on the same straight line from the base of the tower are \( \Large 30 ^{\circ} \) and \( \Large 60 ^{\circ} \), respectively. If the points are separated at a distance of 100 m then the height of the tower is close to
| A). 86.6 m |
| B). 84.6 m |
| C). 82.6 m |
| D). 80.6 m |
|
36). Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
| A). 13 m |
| B). 17 m |
| C). 18 m |
| D). 23 m |
|
37). As seen from the top and bottom of a building of height h m, the angles of elevation of the top of a tower of height \( \Large \frac{\left(3 + \sqrt{3}\right)h}{2}m \) are \( \Large \alpha \) and \( \Large \beta \) respectively.
If \( \Large \beta \) = \( \Large 30 ^{\circ} \), then what is the value of \( \Large \tan \alpha \)?
| A). \( \Large \frac{1}{2} \) |
| B). \( \Large \frac{1}{3} \) |
| C). \( \Large \frac{1}{4} \) |
| D). None of these |
|
38). As seen from the top and bottom of a building of height h m, the angles of elevation of the top of a tower of height \( \Large \frac{\left(3 + \sqrt{3}\right)h}{2}m \) are \( \Large \alpha \) and \( \Large \beta \) respectively. If \( \Large \alpha \) = \( \Large 30 ^{\circ} \), then what is the value of \( \Large \tan \beta \)
| A). 1 |
| B). \( \Large \frac{1}{2} \) |
| C). \( \Large \frac{1}{3} \) |
| D). None of these |
|
39). As seen from the top and bottom of a building of height h m, the angles of elevation of the top of a tower of height \( \Large \frac{\left(3 + \sqrt{3}\right)h}{2}m \) are \( \Large \alpha \) and \( \Large \beta \) respectively. If \( \Large \alpha \) = \( \Large 30 ^{\circ} \) and h = 30 m, then what is the distance between the base of the building, then what is \( \Large \tan \theta \) equal to?
| A). \( \Large 15 + 5\sqrt{3} m \) |
| B). \( \Large 30 + 15\sqrt{3} m \) |
| C). \( \Large 45 + 15\sqrt{3} m \) |
| D). None of these |
|
40). As seen from the top and bottom of a building of height h m, the angles of elevation of the top of a tower of height \( \Large \frac{\left(3 + \sqrt{3}\right)h}{2}m \) are \( \Large \alpha \) and \( \Large \beta \) respectively. If \( \Large \beta \) = \( \Large 30 ^{\circ} \) and if \( \Large \theta \) is the angle of depression of the foot of the tower as seen from the top of the building, then what is \( \Large \tan \theta \) equal to?
| A). \( \Large \frac{ \left(3 - \sqrt{3}\right) }{3\sqrt{3}} \) |
| B). \( \Large \frac{ \left(3 + \sqrt{3}\right) }{3\sqrt{3}} \) |
| C). \( \Large \frac{ \left(2 - \sqrt{3}\right) }{3\sqrt{3}} \) |
| D). None of these |
|
