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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:

129 meter from the foot of a cliff on level of ground, the angle of elevation of the top of a cliff is 30°. The height of this cliff is

A) 50√3 metre B) 45√3 metre
C) 43√3 metre D) 47√3 metre
 
Answer & Explanation Answer: C) 43√3 metre

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1 881
Q:

The angle of elevation of a ladder leaning against a wall is 60 deg and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is

A) 2.3 m B) 4.6 m
C) 9.2 m D) 7.8 m
 
Answer & Explanation Answer: C) 9.2 m

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1 846
Q:

If the elevation of the Sun changes from 30° to 60° , then the difference between the lengths of shadows of a pole 15 m high, is

A) 7.5 m B) 15 m
C) 10√3 m D) 5√3 m
 
Answer & Explanation Answer: C) 10√3 m

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2 846
Q:

The angles of elevation of top and bottom of a flag kept on a flag post from 30 metres distance, are 45 and 30 deg respectively. Height of the flag is [taking √3 = 1.732]

A) 12 √3 m B) 15 m
C) 14.32 m D) 12.68 m
 
Answer & Explanation Answer: D) 12.68 m

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1 837
Q:

Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30 ̊ and 45 ̊ respectively. If the height of the tower is 50 m, the distance between the two men is (Take √3 = 1.73)

A) 136.5 m B) 50 √3 m
C) 100 √3 m D) 135.5 m
 
Answer & Explanation Answer: A) 136.5 m

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1 804
Q:

From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?

A) 720 B) 960
C) 840 D) 1030
 
Answer & Explanation Answer: B) 960

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3 793
Q:

From the top of a 20 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of it's foot is at 45°, then the height of the tower is (√3=1.732)

A) 45.46 m B) 45.64 m
C) 54.64 m D) 54.46 m
 
Answer & Explanation Answer: C) 54.64 m

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0 774
Q:

The upper part of a tree broken over by the wind make an angle of 60 deg with the ground. The distance between the root and the point where top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?

A) 84.14 B) 93.3
C) 98.25 D) 120.24
 
Answer & Explanation Answer: B) 93.3

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2 772