Lakshya Education MCQs

Question: A contractor plans to install two slides for the children to play in a park for elder children. She wants to have a steep slide at a height of 6 m, and inclined at an angle of 60 to the ground. What should be the length of the slide (in m)?
Options:
A.3√3 m
B.5 m
C.4√3 m
D.6 m
Answer: Option C
: C


The above figure represents the given situation.
In the given right-agled triangle,
sin(ACB)=ABACsin60=6ACAC=632=123=43mlengthofslide=43m

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Question 1. A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from 30 to 60 as he walks towards the building. Find the distance he walked towards the building.
  1.    30 m
  2.    20√3 m
  3.    20 m
  4.    30√3 m
Answer: Option B
: B


The situation can be represented by the figure above,
tan(ACB)=ABBCtan60=30BCBC=30tan60=103mtan(ADB)=ABBDtan30=30BDBD=3013=303mDistancewalked=DC=BDBC=303103=203m
Question 2. A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole, if the angle made by the rope with the ground level is 30
___ 

m.

 

:
The figure above represents the given situation.
In the given figure,
sin30=ABACAB=sin30×AC=AC2=302=15m.
Question 3. A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is 30.
  1.    5 m
  2.    15√3 m
  3.    18 m
  4.    20 m
Answer: Option B
: B


The figure above represents the given situation.
From the given firgure,
cos30=BCACBC=AC×cos30=3032
=153m
Question 4. State whether the given statement is true or false:

The angle of depression is the angle between the line of sight of an observer below his horizontal line of sight.
  1.    True
  2.    False
Answer: Option A
: A



The angle of depression is the angle between the line of sight of anobserverbelow his horizontal line of sight.
Question 5. State whether the given statement is true or false:

The angle of elevation is the angle between the line of sight of an observer below his horizontal line of sight.
  1.    True
  2.    False
Answer: Option B
: B

The angle of elevation is the angle between the line of sight of an observer above his horizontal line of sight.
Question 6. A 1.8 m tall man is standing at some distance from a building. The angle of elevation from his eyes to the top of the building increases from 30 to 60 as he walks 20 m towards the building. Find the height of the building (in m).
  1.    10 m
  2.    20√3 m
  3.    20 m
  4.    (10√3 + 1.8) m
Answer: Option D
: D


The situation can be represented by the figure above.
tan(ACB)=ABBCBC=ABtan60.....(1)tan(ADB)=ABBDtan30=ABBC+CDBC+CD=ABtan30.....(2)on subtracting equation(1) from (2)CD=ABtan30ABtan60AB=103
Hence, the height of the building is
= AB + BG = (103+1.8)m.

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