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 Height and Distance Questions

Popular Latest Rated Important Formulae

FACTS  AND  FORMULAE  FOR  HEIGHT  AND  DISTANCE  PROBLEMS

 

 

1.In a right angled ∆OAB, where ∠BOA=θ

 

(i). sinθ =PerpendicularHypotenuse=ABOB

 

(ii). cosθ=BaseHypotenuse=OAOB

 

(iii). tanθ=PerpendicularBase=ABOA

 

(iv). cosecθ =1sinθ=OBAB

 

(v). secθ=1cosθ=OBOA

 

(vi). cotθ=1tanθ=OAAB

 

2. Trigonometrical Identities :

(i). sin2θ+cos2θ=1

(ii). 1+tan2θ=sec2θ

(iii). 1+cot2θ=cosec2θ

 

3. Values of T-ratios :

θ0o30o45o60o90osin θ01212321cos θ13212120tan θ01313Not defined

 

4. Angle of Elevation:

Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O, is called the angle of elevation of P as seen from O.

Therefore, Angle of elevation of P from O is =∠AOP

 

5. Angle of Depression :

Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the angle of depression of P as seen from O.

Q:

The angles of elevation of the top of a tree 220 meters high from two points lie on the same plane are 30° and 45°. What is the distance (in metres) between the two points?

A) 193.22 B) 144.04
C) 176.12 D) 161.05
 
Answer & Explanation Answer: D) 161.05

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3 984
Q:

A helicopter, at an altitude of 1500 m, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 30°respectively. Distance between the two ships, in metres is

A) 1000√3 B) 1000/√3
C) 500√3 D) 500/√3
 
Answer & Explanation Answer: A) 1000√3

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1 958
Q:

Two men standing on same side of a pillar 75 metre high, observe the angles of elevation of the top of the pillar to be 30° and 60° respectively the distance between two men is

A) 100 3m B) 100m
C) 753m D) 253m
 
Answer & Explanation Answer: A) 100 3m

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3 957
Q:

On walking 100 metres towards a building in a horizontal line, the angle of elevation of its top changes from 45 to 60 deg. What will be the height (in metres) of the building?

A) 50(3 + √3) B) 100(√3 + 1)
C) 150 D) 100√3
 
Answer & Explanation Answer: A) 50(3 + √3)

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4 942
Q:

The top of a broken tree touches the ground at a distance of 15 m from its base. If the tree is broken at a height of 8 m from the ground, then the actual height of the tree is

A) 17 m B) 27 m
C) 25 m D) 30 m
 
Answer & Explanation Answer: C) 25 m

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4 938
Q:

The height and the slant height of a right circular cone are 24 cm and 25 cm, respectively. Considering π as 22/7 , find the curved surface area of the said cone.

A) 550 cm2 B) 572 cm2
C) 528 cm2 D) 539 cm2
 
Answer & Explanation Answer: A) 550 cm2

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4 923
Q:

On a ground , there is a vertical tower with a flagpole on its top . At a point 9 m away from the foot of the tower , the angles of elevation of the top and bottom of the flagpole are 60° and 30° respectively . The height of the flagpole is

A) 5√3 m B) 6√3 m
C) 6√2m D) 6√5 m
 
Answer & Explanation Answer: B) 6√3 m

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2 916
Q:

A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to each a window 5m high, then the width of the street is :

A) 17 m B) 16 m
C) 14 m D) 15 m
 
Answer & Explanation Answer: A) 17 m

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4 907