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 observes the elevation of a balloon to be 45° at a point A .He then walks towards the balloon and at a certain place B finds the elevation to be 60°. He further walks in the direction of the balloon and finds it to be directly over him at a height of 450 m. Distance travelled from A to B is

A - 300√3 m

B - 200√3 m

C - 100√3 m

D - 450√3 m

Answer : A

Explanation

Height & Distance Solution 2

450/BD= tan (60) =>BD =450/√3
450/AD= tan (30) =>AD= 450√3
AD =BD +AB
=>AB=AD-BD= 450√3-450/√3=(450x3-450)/√3=300√3m

Q 2 - When the sun's altitude changes from 45° to 60°, the length of the shadow of a tower decreases by 45m. What is the height of the tower?

A - (45√3)/(√3-1)

B - (45√3)/(√3+1)

C - (45+√3)/(√3-1)

D - (45-√3)/(√3-1)

Answer : A

Explanation

Height & Distance Solution 6

Let AD be the tower, BD be the initial shadow and CD be the final shadow.
Given that BC = 45 m,  ABD = 45°,  ACD = 60°,
Let CD = x, AD = h
From the right   CDA, tan60=h/x
From the right   BDA, tan45=(45+x)/h=>h=45+x
=>h=45+h/√3
=>h(1-1/√3)=45
=>h=45/(1-1/√3)=(45√3)/(√3-1)

Q 3 - A man in a boat is rowing away from a cliff (180 meters high), take 90 seconds to change angle of elevation of the top of cliff from 30° to 45°.The speed of the boat is

A - 2(√3) m/sec

B - 3(√3-1) m/sec

C - 2(√3-1) m/sec

D - (√3-1) m/sec

Answer : C

Explanation

Height & Distance Solution 8

From right angled triangle ADB,
Tan45=AB/AD =>AB=AD=180
 From right angled triangle ACB,
Tan 30=180/(CD+180)
=>CD+180=180√3
=>CD=180(√3-1)
Speed =Distance/Time=180(√3-1)/90=2(√3-1) m/sec

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 - The point of height of a tower from a separation 50 m from its foot is 30. The tower's tallness is:

A - 50√3m

B - 50/√3m

C - 23√3m

D - 100m/√3

Answer : B

Explanation

Height & Distance Solution 16

Let AB be the tower and AC be the even line such that AC=50 m and ∠ACB=30°.
AB/AC=tan 30°=1/√3
=>x/50 = 1/√3
> x=50*1/√3m= 50/√3m.
∴ Height of the tower=50/√3m.

Q 7 - The point of the height of a stepping stool inclining toward a divider is 60°and the step's foot is 7.5 m far from the divider. The stepping stool's length is

A - 15 m

B - 14.86 m

C - 15.64 m

D - 15.8 m

Answer : A

Explanation

Height & Distance Solution 19

Let AB be the step inclining toward the divider CB.
Let AC be the flat such that AC=7.5M
What's more, ∠CAB=60°
∴ AB/AC=sec60°=2 => AB/7.5m=2 => AB=15m.
∴ length of the stepping stool is 15m.

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.


aptitude_height_distance.htm

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