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Quantitative Aptitude

HEIGHT AND DISTANCE MCQs

Total Questions : 206 | Page 1 of 21 pages
Question 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 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

  1.    173m
  2.    200m
  3.    273m
  4.    300m
 Discuss Question
Answer: Option C. -> 273m

Let AB be the lighthouse and C and D be the positions of the ships.


Two Ships Are Sailing In The Sea On The Two Sides Of A Light...


Then,\(AB=100m, \angle ACB=30^{0} and \angle ADB=45^{0}
\)


\(\frac{AB}{AC}=\tan30^{0}=\frac{1}{3}\Rightarrow AC=AB\times3=1003m.\)


\(\frac{AB}{AD}=\tan45^{0}=1 \Rightarrow AD=AB=100m.\)


Therefore CD=\(\left(AC+AD\right)=\left(1003+100\right)m\)


 = 100(3 + 1)


= (100 x 2.73) m


= 273 m

Question 2.

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the mans eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

  1.    43 units
  2.    8 units
  3.    12 units
  4.    Data inadequate
  5.    None of these
 Discuss Question
Answer: Option D. -> Data inadequate

One of AB, AD and CD must have given.


A Man Standing At A Point P Is Watching The Top Of A Tower, ...


So, the data is inadequate.

Question 3.

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

  1.    2.3 m
  2.    4.6 m
  3.    7.8 m
  4.    9.2 m
 Discuss Question
Answer: Option D. -> 9.2 m

Let AB be the wall and BC be the ladder.


The Angle Of Elevation Of A Ladder Leaning Against A Wall Is...


=Then, \(\angle ACB = 60^{0} and AC=4.6m.\)


\(\frac{AC}{BC}=\cos 60^{0}=\frac{1}{2}\)


BC =  2 x AC


= (2 x 4.6) m


= 9.2 m.

Question 4.

An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is:

  1.    21.6 m
  2.    23.2 m
  3.    24.72 m
  4.    None of these
 Discuss Question
Answer: Option A. -> 21.6 m

Let AB be the observer and CD be the tower


An Observer 1.6 M Tall Is 203 away From A Tower. The Angle ...


\(Draw BE\bot CD.\)


Then, CE = AB = 1.6 m,


      BE = AC = 203 m.


\(\frac{DE}{BE}=\tan30^{0}=\frac{1}{3}\)


\(\Rightarrow DE = \frac{203}{3}m=20m.\)


Therefore CD = CE + DE = (1.6 + 20) m = 21.6 m.

Question 5.

From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

  1.    149 m
  2.    156m
  3.    173m
  4.    200m
 Discuss Question
Answer: Option C. -> 173m

Let AB be the tower.


From A Point P On A Level Ground, The Angle Of Elevation Of ...


Then,\(\angle APB =30^{0} and AB = 100m\)


\(\frac{AB}{AP} = \tan30^{0}=\frac{1}{3}\)


AP = (AB x 3) m


= 1003 m


= (100 x 1.73) m


= 173 m.

Question 6.

The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:

  1.    \(30^{0}\)
  2.    \(45^{0}\)
  3.    \(60^{0}\)
  4.    \(90^{0}\)
 Discuss Question
Answer: Option A. -> \(30^{0}\)

Let AB be the tree and AC be its shadow.


The Angle Of Elevation Of The Sun, When The Length Of The Sh...


\(Let \angle ACB=\theta\)


\(Than,\frac{AC}{AB}=3 \Rightarrow \cot\theta=3\)


\(\therefore \theta=30^{0}\)

Question 7.

When the length of the shadow of a pole is equal to a height of the pole, then  the elevation of source of light is

  1.    \(30^{0}\)
  2.    \(45^{0}\)
  3.    \(60^{0}\)
  4.    \(90^{0}\)
 Discuss Question
Answer: Option B. -> \(45^{0}\)

Let  angle of elevation  of  right angle   triangle ABC of angle C = θ


                                                   and   height AB =  shadow BC = x


                                                   tan θ  =  \(\frac{AB}{BC}=\frac{x}{x}=1=45^{0}\)

Question 8.

The angle  of elevation of the sun, if the length of the shadow of a tower is   √3 times the height of the towre is 

  1.    \(30^{0}\)
  2.    \(45^{0}\)
  3.    \(60^{0}\)
  4.    \(90^{0}\)
 Discuss Question
Answer: Option A. -> \(30^{0}\)

Let in right angle triangle ABC of angle C = θ


height AB = x and shadow  BC = √3 x


 tan θ = \(\frac{AB}{BC}=\frac{x}{\sqrt{3}x}=\frac{1}{\sqrt{3}}=30^{0}\)

Question 9.

the top of two poles of height 20 m and 14 m are cnected by a wire . if the wire makes an angle of 300 with horizontal , then the length of the wire is 

  1.    8 m
  2.    10 m
  3.    12 m
  4.    14 m
 Discuss Question
Answer: Option C. -> 12 m

lat pole AB = 14 m


     pole CD = 20 m


CD – AB = DE


20 m -14 m =  6 m


sin \(30^{0}=\frac{DE}{BD}=\frac{6}{BD} \)


\(\frac{1}{2}=\frac{6}{BD}\)


\(BD=6\times2= 12\)m

Question 10. A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true?
  1.    h3 - 50h2 + (200)2h + (200)250 = 0
  2.    h3 - 50h2 - (200)2h + (200)250 = 0
  3.    h3 + 50h2 + (200)2h - (200)250 = 0
  4.    None of these
 Discuss Question
Answer: Option C. -> h3 + 50h2 + (200)2h - (200)250 = 0

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