51). The angle of elevation of the top of a chimney and roof of the building from a point on the ground are x and 45° respectively. The height of building is h metre. Then the height of the chimney (in metre) is
| A). h cot x + h |
| B). h cot x - h |
| C). h tan x - h |
| D). h tan x + h |
|
52). There are two vertical posts, one on each side of a road, just opposite to each other. One post is 108 metre high. From the top of this post the angle of depression of the top and foot of the other post are 30° and 60° respectively. The height of the other post (in metre) is
| A). 36 |
| B). 72 |
| C). 108 |
| D). 110 |
|
53). The angle of elevation of the top of a tower from two points A and B lying on the horizontal through the foot of the tower are 15° and 30° respectively. If A and B are on the same Side of the tower and AB = 48 meter then the height of the tower is;
| A). \( \Large 25\sqrt{3}\ meter \) |
| B). \( \Large 24\ meter \) |
| C). \( \Large 24\sqrt{2}\ meter \) |
| D). \( \Large 96\ meter \) |
|
54). Two posts are x metres apart horizontally and the height of one is double that of the other. If from the mid-point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is
| A). \( \Large \frac{x}{2\sqrt{2}} \) |
| B). \( \Large \frac{x}{4} \) |
| C). \( \Large x\sqrt{2} \) |
| D). \( \Large \frac{x}{2} \) |
|
55). An aeroplane when flying at a height of 5000m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. The vertical distance between the aeroplanes at that instant is
| A). \( \Large 5000 \left(\sqrt{3}-1\right) m \) |
| B). \( \Large 5000 \left(3-\sqrt{3}\right) m \) |
| C). \( \Large 5000 \left(1-\frac{1}{\sqrt{3}}\right)m \) |
| D). \( \Large 4500\ m \) |
|
56). A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance towards the tower and then his angle of elevation of the top of the tower is 60°. If the height of tower is 30m, then the distance he moves is
| A). \( \Large 22\ m \) |
| B). \( \Large 23\sqrt{3}\ m \) |
| C). \( \Large 20\ m \) |
| D). \( \Large 20\sqrt{3}\ m \) |
|
57). An aeroplane when flying at a height of 3125m from the ground passes vertically below another plane at an instant when the angle of elevation of the two planes from the same point on the ground an 30° and 60° respectively. The distance between the two planes at that instant is
| A). 6520 m |
| B). 6000 m |
| C). 5000 m |
| D). 6250 m |
|
58). The shadow of the tower becomes 60 meters longer when the altitude of the sun changes from 45° to 30°. Then the height of the tower is
| A). \( \Large 20(\sqrt{3}+1)m \) |
| B). \( \Large 24(\sqrt{3}+1)m \) |
| C). \( \Large 30(\sqrt{3}+1)m \) |
| D). \( \Large 30(\sqrt{3}-1)m \) |
|
59). A vertical post 15 ft. high is broken at a certain height and its upper part, not completely separated meets the ground at an angle of 30". Find the height at which the post is broken
| A). \( \Large 10ft \) |
| B). \( \Large 5ft \) |
| C). \( \Large 15\sqrt{3}(2-\sqrt{3})ft \) |
| D). \( \Large 5\sqrt{3}ft \) |
|
60). The shadow of a tower is \( \Large \sqrt{3} \) times its height . Then the angle of elevation of the top of the tower is
| A). 45° |
| B). 30° |
| C). 60° |
| D). 90° |
|
