#### Height and Distance MCQ Questions and answers-

##### 1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Explanation:
```Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB	= tan 30° =	1	         AC = AB x 3 = 1003 m.
AC	3
AB	= tan 45° = 1          AD = AB = 100 m.
CD = (AC + AD)	= (1003 + 100) m
= 100(3 + 1)
= (100 x 2.73) m
= 273 m.
```

##### 2. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
Explanation:
```One of AB, AD and CD must have given. ```

##### 3. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Explanation: Let AB be the wall and BC be the ladder.
``` Then, ACB = 60° and AC = 4.6 m.

AC	= cos 60° =	1
BC	2
BC	= 2 x AC
= (2 x 4.6) m
= 9.2 m.
```

##### 4. An observer 1.6 m tall is 20 root 3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The heights of the tower is:
Explanation: Let AB be the observer and CD be the tower.
``` Draw BE  CD.

Then, CE = AB = 1.6 m,

BE = AC = 203 m.

DE	= tan 30° =	1
BE	3
DE =	203	m = 20 m.
3
CD = CE + DE = (1.6 + 20) m = 21.6 m.
```

##### 5. From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:
Explanation:
```Let AB be the tower. Then, APB = 30° and AB = 100 m.

AB	= tan 30° =	1
AP	3
AP	= (AB x 3) m
= 1003 m
= (100 x 1.73) m
= 173 m.
```

##### 6. A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?  