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 step inclining toward a vertical divider makes a point of 45 with the even ground. The step's Foot is 3m from the divider. Find Length of the step?

A - 4.23 m

B - 5.23 m

C - 6.23 m

D - 7.23 m

Answer : A

Explanation

Height & Distance Solution 11

Let AB be the step and BC be the divider and let AC be the even ground.
Then, ∠CAB=45 and AC=3m. Let AB= x Meter.
From right △ ACB, we have
AB/AC =sec. 45° = √2 => x/3 = √2
X= 3√2m = (3*1.41) m= 4.23m.
∴ Length of the stepping stool is 4.23 m

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 - At a moment, the shadow's length of a shaft is √3 times the stature of the shaft. The edge of rise of the sun is:

A - 30°

B - 45°

C - 60°

D - 75°

Answer : A

Explanation

Height & Distance Solution 17

Let AB be the post and AC be its shadow.
Let AB =X m. Then, AC= √3Xm.Let∠ACB=θ.
AB/AC=tanθ => tanθ = X/√3X = 1/√3 =tan30°.
∴ θ = 30°.
Hence, the point of rise is 30°.

Q 7 - From The highest point of a bluff 90 m high, the edges of Misery of the top and base of a tower are seen to be 30° and 60°. What is the tower's tallness is?

A - 30 m

B - 45 m

C - 60 m

D - 75 m

Answer : C

Explanation

Height & Distance Solution 21

Let AB be the precipice and CD be the tower. Draw DE || CA.
Then, ∠BDE=30°, ∠BCA=60°and AB= 90m.
From right △CAB, we have
CA/AB=cost60°=1/√3 => CA/90=1/√3
=>CA=(90*1/√3* √3/√3)
=30 √3m.
∴ DE =CE=30/√3m.
From right ?DEB, we have
BE/DE= tan30°=1/√3 => BE/30 √3=1 √3
=>BE= (30 √3*1 √3) =30m.
∴ CD=AE= (AB-BE) = (90-30) m=60m.
Hence, the tower's stature is 60m.

Q 8 - The stature of a tree is 10m. It is twisted by the wind in a manner that its top touches the ground and makes a point of 60 with the ground. At what range from base did the tree get twisted? (√3=1.73)

A - 4.6m

B - 4.8m

C - 5.2m

D - 5.4m

Answer : A

Explanation

Height & Distance Solution 23

Let AB be the tree bowed at the point C so that part CB takes the position CD.
Then ,CD=CB. Let AC=x meters. At that point, CD = CB= (10-X) m and ∠ADC=60°.
AC/AC=sin60° => x/(10-x) = √3/2
=>2x=10 √3-√3x
=> (2+ √3) x= 10 √3
=>x=10 √3/ (2+ √3)*(2-√3)/(2-√3)=20 √3-30)m
= (20*1.73-30) m=4.6m
=> Required height=4.6m.


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