Aptitude - Height & Distance Online Quiz



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Following quiz provides Multiple Choice Questions (MCQs) related to Height & Distance. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Questions and Answers

Q 1 - A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 10 minutes for the angle of depression to change from 45° to 60°, how soon after this will the car reach the observation tower?

A - 10 min 30 sec

B - 13 min 20 sec

C - 15 min 10 sec

D - 16 min 30 sec

Answer : B

Explanation

Height & Distance Solution 3

Let AB be the tower and C and D be the two positions of the car.
Then,from figure
AB/AC=tan 60 =√3 => AB=√3AC
AB/AD=tan 45=1 => AB=AD
AB=AC+CD
CD=AB-AC=√3AC - AC=AC (√3-1)
CD = AC (√3-1) =>10 min
 AC=> ?
AC/(AC(√3-1)) x 10=?=10/(√3-1)=13.66=13 min 20 sec(approx)

Q 2 - A vertical pole fixed to the ground is divided in the ratio 1:4 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 16 m away from the base of the pole, what is the height of the pole?

A - 8√2

B - 30√2

C - 40√2

D - 50√2

Answer : C

Explanation

Height & Distance Solution 4

Let CB be the pole and point D divides it such that BD : DC = 1 : 4 = X:4X
Given that AB = 16 m
Let the the two parts subtend equal angles at point A such that
CAD =  BAD = Θ
=>tan  Θ=X/16 =>X=16 tan ( Θ) ------ (1)
=>tan( Θ+  Θ)=4X/16
=>16 tan (2 Θ)=4X
=>16(2tan ( Θ))/(1-tan ( Θ)2)=4X ------ (2)
From eqn 1 & 2 2X/(1-tan ( Θ)2)=4X (X=16tan Θ)
1/(1-(X/16)2)=2
1-(X/16)2=1/2=>162-
X2=162/2=>X2=128
=>X=8√2
=>Height of pole BC = X+4X=5X=40√2

Q 3 - From the top of mast head of height 210 meters of a ship, a boat is observed at an angle of depression of 30° then the distance between them is

A - 210√3

B - 210/√3

C - 70√3

D - 105√3

Answer : A

Explanation

Height & Distance Solution 7

From the right angled triangle CAB
Tan(30) =210/X
=>X=210/Tan(30)=210/(1/√3)=210√3

Q 4 - A flag staff of 10 meters height stands on a building of 50 meters height. An observer at a height of 60 meters subtends equal angles to the flag staff and the building. The distance of the observer from the top of the flag staff is

A - 2√6

B - 3√6

C - 5√6

D - √6

Answer : C

Explanation

Height & Distance Solution 10

From the figure
tanθ=10/CB
tan(2θ)=60/CB=(2tan(θ))/(1-tan(θ)2)
=>60/CB=(2tan(θ))/(1-tan(θ)2)=(2(10/CB))/(1-(10/CB)2)
=>3/1=1/(1-(10/CB)2)
=>3x(1-(10/CB)sup>2)=1
3CB2-300=CB2
2CB2=300=>CB=√150=5√6

Q 5 - Consider vertical shaft 6 m high has a shadow of length 2√3m, discover the angle of elevation of the sun?

A - 60°

B - 30°

C - 40°

D - 50°

Answer : A

Explanation

Height & Distance Solution 13

Let AB be the building and AC be its shadow. Then, AB= 6m and AC= 2√3m.
Let ∠ACB= θ Then tan θ = AB/AC= 6/2√3m
 =√3= >θ =60°
Point of rise of the sun is 60°

Q 6 - A 10 m long stepping stool is put against a divider. It is slanted at a point of 30°to the ground. The separation of the stepping stool's foot from the divider is:

A - 7.32 m

B - 8.26 m

C - 8.66 m

D - 8.16 m

Answer : C

Explanation

Height & Distance Solution 18

Let AB be the step slanted at 30°to the Ground AC.
Then, AB=10m and 

Q 7 - A kite is flying at a tallness of 75 m from the level of ground, joined to a string slanted at 60° to the level. The string's length is:

A - 50 √2 m

B - 50√3 m

C - 50m/√2

D - 50m/√3

Answer : B

Explanation

Height & Distance Solution 20

Let AB be the kite and AC be the level ground
So that BC - AC.
At that point, ∠BAC=60°and BC=75m. Let AB=x meters.
Presently AB/BC=coses60°=2/ √3
=> x/75=2/√3 =>x=150/√3 =150* √3/3=50 √3m.
∴ Length of the string=50 √3m.

Q 8 - On the level plane, there is a vertical tower with a flagpole on its top. At a point 9m far from the tower, the edges of rise of the top and Base of the flagpole are 60°and 30°respectively.The flagpole's tallness is:

A - 6 √3 m

B - 5 √3m

C - 6 √2m

D - 4m

Answer : A

Explanation

Height & Distance Solution 25

Let AB be the tower and BC be the flag pole and let O be the point of observation.
Then, A=9m, ∠AOB=30°and ∠AOC=60°
AB/OA=tan30°=1 ∠ =>AB/9=1∠
=>AB=(9*1/ √3* √3/√3)= 3 √3m.
AC/AO=tan60°=√3 =>AC/9= √3 =>AC= 9√3m.
∴BC= (AC-AB) = (9 √3-3 √3) m=6 √3m.
∴ Height of the flagpole is 6 √m.


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