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Aptitude - Height & Distance Online Quiz
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.
Q 1 - The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Answer : D
Explanation
Let AB be the wall and BC be the ladder. Then, ∠ACB = 45° and AC = 7.5 m AC/BC= Cos (45) =1/√2 BC=7.5√2
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?
Answer : C
Explanation
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
Answer : A
Explanation
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
Answer : C
Explanation
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 - From The highest point of a 10 m high building, the edge of rise of the of the highest point of a tower is 60° and the despondency's edge of its foot is 45°,Find The tower's stature. (take√3=1.732)
Answer : D
Explanation
Let AB be the building and CD be the tower. Draw BE perpendicular to CD. At that point CE =AB = 10m, ∠EBD= 60° and ∠ACB= ∠ CBE=45° AC/AB= cot45°=1 = >AC/10 =1 => AC = 10m. From △ EBD, we have DE/BE= tan 60°=√3 => DE/AC= √3 => DE/10= 1.732 =>DE = 17.3 Height of the tower = CD= CE+DE= (10+17.32) = 27.3 m.
Q 6 - The point of height of a tower from a separation 50 m from its foot is 30. The tower's tallness is:
Answer : B
Explanation
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
Answer : A
Explanation
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 - From a point on a scaffold over the waterway, the edge of dejection of the banks on inverse sides of the waterway is 30°and 45°respectively. In the event that the scaffold is at tallness of 2.5m from the banks, find the width of the Stream. (Take √3=1.732)
Answer : B
Explanation
Let and B be two point on the banks on inverse sides of the stream. Let P be a point on the scaffold at stature of 2.5m. Let PQ-AB. PQ=2.5m.∠BAP=30°and ∠ABP=45°. QB/PQ=cot45°=1 => QB/2.5=1 => QB=2.5m. AQ/PQ =cot30°=√3 => AQ/2.5= √3 => AQ= (2.5)√3m. Width of the stream =AB= (AQ+QB)=2.5(√3+1) 5/2(1.732+1) m=6.83m.
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