- Aptitude - Home
- Aptitude - Overview
- Quantitative Aptitude
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 - 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
Answer : A
Explanation
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 - 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 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?
Answer : A
Explanation
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?
Answer : A
Explanation
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:
Answer : A
Explanation
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 - 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:
Answer : B
Explanation
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 - 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)
Answer : A
Explanation
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.