Height and Distance Questions

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:

Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30 and 60 deg respectively. The distance between the persons is

A) 173.2m B) 100m
C) 157.7m D) 273.2m
 
Answer & Explanation Answer: A) 173.2m

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Q:

The upper part of a tree broke at a certain height makes an angle of 60 ° with the ground at a distance of 10 m. from its feet. The original height of the tree was

A) 20√3 m. B) 10√3 m.
C) 10(2+√3) m. D) 10(2-­√3) m.
 
Answer & Explanation Answer: C) 10(2+√3) m.

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Q:

The angles of elevation of the top of a tower 72 metre high from the top and bottom of a building are 30° and 60° respectively. What is the height (in metres) of building?

A) 42 B) 20√3
C) 24√3 D) 48
 
Answer & Explanation Answer: D) 48

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Q:

A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36 m from the bank, he finds that the angle is 30°. The breadth of the river is

A) 15 m B) 18 m
C) 16 m D) 11 m
 
Answer & Explanation Answer: B) 18 m

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Q:

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is

A) 4 m B) 7 m
C) 9 m D) 6 m
 
Answer & Explanation Answer: D) 6 m

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Q:

From the top of a platform 5 m high, the angle of elevation of a tower was 30 deg. If the platform was positioned 40√3 m away from the tower, how tall was the tower?

A) 40 m B) 20√3 m
C) 30√3 m D) 45 m
 
Answer & Explanation Answer: D) 45 m

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Q:

If the length of the shadow of a vertical pole on the horizontal ground is √3 times its height, then the angle of elevation

A) 40 deg B) 50 deg
C) 30 deg D) 45 deg
 
Answer & Explanation Answer: C) 30 deg

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Q:

A 25m long ladder is rested on a wall. The foot of the ladder is 7m away from the wall. If the end of the ladder (resting on the wall) slides down 4m, then how far will its foot move away?

A) 5 m B) 8 m
C) 9 m D) 10 m
 
Answer & Explanation Answer: B) 8 m

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