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:
Veiw Answer
Answer: 273
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.
AD
 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?
Veiw Answer
Answer: Data inadequate
Explanation:
One of AB, AD and CD must have given.



So, the data is inadequate.

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:
Veiw Answer
Answer: 9.2 m
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:
Veiw Answer
Answer: 21.6 m
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:
Veiw Answer
Answer: 156 m
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?
Veiw Answer
ANSWER: 50(root3 - 1)/ root3 m Explanation:

7. A tree is cut partially and made to fall on ground. The tree however does not fall completely and is still attached to its cut part. The tree top touches the ground at a point 10m from foot of the tree making an angle of 30°. What is the length of the tree?
Veiw Answer
ANSWER: 103 m
Explanation: