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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:

A tower is broken at a point P above the ground. The top of the tower makes an angle 60° with the ground at Q. From another point R on the opposite sideof Q angle of elevation of point P is 30°. If QR = 180 m, then what is the total height (in metres) of the tower?

 

A) 90 B) 45√3
C) 45(√3+1) D) 45(√3+2)
 
Answer & Explanation Answer: D) 45(√3+2)

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7 2059
Q:

A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?

A) 6.2 m B) 6.5 m
C) 6.8 m D)  7.5 m
 
Answer & Explanation Answer: B) 6.5 m

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10 1838
Q:

There are two parallel streets each directed north to south. A person in the first street travelling from south to north wishes to take the second street which is on his right side. At some place, he makes a 150 deg turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60 deg and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?

A) 7.5 km B) 10.5 km
C) 12.5 km D) 15 km
 
Answer & Explanation Answer: C) 12.5 km

Explanation:
Initially the person is travelling from south to north i.e. D to A
He takes 150 deg right turn and moves AB distance and then he takes 60 deg left turn travels BC
AB = 20km/hr * 15/60 hr = 5km
BC = 30 * 20/60 = 10 km
We know that distance between both the streets is DC = DB + BC
DB = AB cos 60o= 5. ½ =2.5 km
So the distance between streets = 12.5 km
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5 1797
Q:

A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60 to 45 deg. What is the height (in metres) of the lighthouse?

A) 240√3 B) 480[(√3) – 1]
C) 360√3 D) 280√2
 
Answer & Explanation Answer: A) 240√3

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4 1545
Q:

Angle of Elevation means

Answer

In Heights and Distances,


The angle of elevation of an object is the angle between the horizontal and the line of sight that is the line from the object to the observer's eye.

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8 1339
Q:

The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is 5/9 metres, then what is the distance (in metres) between the two poles?

A) 63 B)  30
C) 25 D) 45
 
Answer & Explanation Answer: D) 45

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6 1192
Q:

The height of a tower is 300 meters. When its top is seen from top of another tower,then the angle of depression is 60°. The horizontal distance between the bases of the two towers is 120 metres. What is the height (in metres) of the small tower?

A) 88.24 B) 106.71
C) 92.15 D) 112.64
 
Answer & Explanation Answer: C) 92.15

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4 1122
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 1081