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- Question
- A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance (in m) traveled by the car during this time is :
Options- A. 100 ?3
- B. 200 ?3 3
- C. 100 ?3 3
- D. 200 ?3
- Correct Answer
- 200 ?3 3
Explanation
- 1. A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before. The height of the tower is :
Options- A. 80 m
- B. 100 m
- C. 160 m
- D. 200 m Discuss
- 2. From a point P on a level ground, the angle of elevation of the top of the tower is 30°. If the tower is 100 m high, the distance of the point P from the foot of the tower is :
Options- A. 100/ ?3 m
- B. 100 ?3 m
- C. 50?3 m
- D. 50/?3 m Discuss
- 3. The angle of elevation of the top of a tower at a point G on the ground is 30°. On walking 20 m towards the tower, the angle of elevation becomes 60°. The height of the tower is equal to :
Options- A. 10 m ?3
- B. 20 ?3 m
- C. 20 m ?3
- D. 10 ?3 m Discuss
- 4. The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45°. If the elevation of the top at the same point is to be 60°, the tower must be raised to a height :
Options- A. 120 ( ?3 + 1 ) m
- B. 120 ( ?3 - 1 ) m
- C. 10 ( ?3 + 1 )
- D. None of these Discuss
- 5. A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 40 m from the bank, he finds the angle to be 30°. The breadth of the river is :
Options- A. 40 m
- B. 60 m
- C. 20 m
- D. 30 m Discuss
- 6.
sin A + sin A is ( 0° < A < 90° ) . 1 + cos A 1 - cos A
Options- A. 2 cosec A
- B. 2 sec A
- C. 2 sin A
- D. 2 cos A Discuss
- 7. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
Options- A. 2.3 m
- B. 4.6 m
- C. 7.8 m
- D. 9.2 m Discuss
- 8. From the top of h meter high cliff the angles of depression of the top and the button of a tower are observed to be 30° and 60° respectively. The height of the tower is?
Options- A. h?3
- B. 2h?3
- C. h/3
- D. 2h/3 Discuss
- 9. The angles of elevation of the top of a verticle tower from two points, distance a and b (a > b) from the base and in the same straight line with it are complementary. Then the height of the tower is?
Options- A. ?(ab)
- B. ?(a2 + b2)
- C. ?(a2 - b2)
- D. ?a(a - b) Discuss
- 10. The angle of elevation of the top of a tower standing on a horizontal plane from a point A is ?. After walking a distance a towards the foot of the tower, the angle of elevation is found to be ?. The height of the tower is :
Options- A. a Sin ? Sin ?/ Sin(? - ?)
- B. a Sin ? Sin ?/Sin(? - ?)
- C. a Sin( ? - ? ) Sin ? Sin ?
- D. a Sin(? - ?)/Sin ?Sin ? Discuss
Height and Distance problems
Search Results
Correct Answer: 80 m
Explanation:
Correct Answer: 100 ?3 m
Explanation:
Correct Answer: 10 ?3 m
Explanation:
Correct Answer: 120 ( ?3 - 1 ) m
Explanation:
Correct Answer: 20 m
Explanation:
Correct Answer: 2 cosec A
Explanation:
Correct Answer: 9.2 m
Explanation:
Let AB be the wall and BC be the ladder.
Then, ? ACB = 60° and AC = 4.6 m.
AC/BC = cos 60° = 1/2
BC = 2 x AC
= (2 x 4.6) m
= 9.2 m.
Correct Answer: 2h/3
Explanation:
Let us draw a figure below as per given question.
Let AB = h meter be the height of cliff and CD = x meter be the height of the tower and also ? ADB = 60° and ?ACE = 30° ,
Now, from the figure, AE = (h - x) meter
From right triangle ABD, BD = h cot 60° = h/?3 m
From right triangle CEA. (h - x) = EC tan 30° = BD tan 30°
? h - x = h/?3 X 1/?3
? x = h - h/3 = 2h/3 meter
Correct Answer: ?(ab)
Explanation:
Let CD = h unit be the height of the tower and A and B be the two points on the ground, such that DA = a; DB = b;
? DAC = ? and ?DBC = 90° - ?
From right triangle ADC, CD = h = a tan ? ...(i)
From right triangle BDC, CD = h = b tan (90° - ? ) = b cot ? .......(ii)
Multiplying equations (i) and (ii), we get
h2 = a tan ? X b cot?
Hence, h = ?ab
Correct Answer: a Sin ? Sin ?/ Sin(? - ?)
Explanation:
Let OP be the tower of height h (say) and A and B be the two positions on the horizontal line through O, such that
?OAP = ?, ?OBP = ? and OB = x
In ?OBP, Use the trigonometry formula
Tan? = P/B = Perpendicular distance / Base distance
Tan? = OP/OB
? OB = OP/Tan?
? OB = OP Cot?
Put the value of OB and OP , We will get
x = h Cot ?...............(1)
In ?OAP, Similarly
Tan? = OP/OA
? OA = OP/ Tan?
? OA = OP Cot ?
Put the value of OA and OP
? a + x = h Cot ?
? x = h Cot ? - a ............(2)
From equation (1) and (2)
? h Cot ? = h Cot ? - a
? a = h Cot ? - h Cot ?
? a = h (Cot ? - Cot ?)
? a = h (Cos ?/ Sin ? - Cos ? / Sin ? )
? a = h( (Cos ? Sin ? - Cos ? Sin ? ) /Sin ? Sin ? )
? a = h( Sin(? - ?) / Sin ? Sin ?)
? h = a Sin ? Sin ?/ Sin(? - ?)
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