Height and Distance Mathematic
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| Height and Distance Mathematic |
Important information:- It is an important application of trigonometry which helps us to find the height of any object and distance of that object from any point which are not directly measurable. If the angle of elevation/ depression from a point is known.
Line of Sight:- A line of sight is the line drawn from the eye of an observer to the point, where the object is viewed by the observer.
Horizontal Line:- The line of sight which is parallel to ground level is known as horizontal line.
Table of Contain:-
1. What is the angle of elevation of the Sun when the shadow of a pole is √3 times the length of the pole ?
(a) 30°
(b) 45°
(c) 60°
(d) None of these
Answer :- (a) 30°
2. The shadow of a tower is 15 m, when the Sun's elevation is 30°. What is the length of the shadow, when the Sun's elevation is 60° ?
(a) 3 m
(b) 4 m
(c) 5 m
(d) 6 m
Answer :- (c) 5 m
3. What is the angle of elevation of the Sun, when the shadow of a pole of height x m is —m√3 ?
(a) 30°
(b) 45°
(c) 60°
(d) 75°
Answer :- (c) 60°
4. A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time, a tower casts a shadow of 40 m long on the ground. The height of the tower is [SSCCGL2012]
(a) 60 m
(b) 65 m
(c) 70 m
(d) 72 m
Answer :- (a) 60 m
5. The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is [SSCCCL2012]
(a) 8√3 m
(b) 8 m
(c) 6√3 m
(d) 6 m
Answer :- (a) 8√3 m
6. The shadow of a tower standing on a level plane is found to be 50 m longer when the Sun's elevation is 30°. When it is 60°, then what is the height of the tower? [CDS 2014]
(a) 25m
(b) 25√3m
(c) 25/√3m
(d) 30m
Answer :- (c) 25/√3m
7. The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°. What is the height of the tower, to the nearest meter?
(a) 48 m
(b) 49 m
(c) 50 m
(d) 51 m
Answer :- (c) 50 m
8. The angles of depression from the top of a light house of two boats are 45° and 30° towards the west. If the two boats are 5 m apart, then the height of the light house is [SSCFCI2012]
(a) (2.5√3 - 1) m
(b) 2.5(√3 - 1) m
(c) (2.5√3 + 1) m
(d) 2.5(√3 + 1) m
Answer :- (d) 2.5(√3 + 1) m
9. The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is 30°. If the angle of elevation at the same point is to be 45°, then the pillar has to be raised to a height of how many meters?
(a) 59.4 m
(b) 61.4 m
(c) 62.4 m
(d) 63.4 m
Answer :- (d) 63.4 m
10. From the top of a cliff 200 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45°, respectively. What is the height of the tower? [CDS 2012]
(a) 200 m
(b) 200{(√3 - 1)/ √3} m
(c) 200√3 m
(d) None of these
Answer :- (b) 200{(√3 - 1)/ √3} m
