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- Question
- In a rectangle, if the angle between a diagonal and a side is 30° and the length of diagonal is 6 cm, the area of the rectangle is :
Options- A. (a) 9 cm2
- B. 9 ?3 cm2
- C. 27 cm2
- D. 36 cm2
- Correct Answer
- 9 ?3 cm2
Explanation
- 1. The upper part of a tree broken by the wind makes an angle of 30° with the ground and the distance from the root to the point where the top of the tree touches the ground is 10 m. What was the height of the tree?
Options- A. 10?3
- B. 10/ ?3
- C. 20 ?3
- D. None of these Discuss
- 2. A tower stands on a horizontal plane. A man on the ground 100 m from the base of the tower finds the angle of elevation of the top of the tower to be 30°. What is the height of the tower?
Options- A. 100 m
- B. 100 ?3
- C. 100/ ?3
- D. None of these Discuss
- 3. At a point on a level plane a tower subtends an angle ? and a flag-staff a ft. in length at the top of the tower subtends an angle ?. The height of the tower is :
Options- A. asin ? cos ? / cos ( ? + ? )
- B. asin ? cos ( ? + ? ) / sin ?
- C. a cos ( ? + ? ) / sin ? sin ?
- D. None of these Discuss
- 4. The height of the center of the round balloon of radius r, which subtend an angle ? at the eye of an observer and the elevation of whose center from the eye is ?, is given by?
Options- A. r Sin ? Sin ?
- B. r Cosec ?/2 Sin ?
- C. r Cosec ? Sin ?
- D. None of these Discuss
- 5. ABCD is a square plot. The angle of elevation of the top of a pole standing at D from A or C is 30° and that from B is ? then Tan ? equal to?
Options- A. ?6
- B. 1/?6
- C. ?3/?2
- D. ?2/?3 Discuss
- 6. From the top of a lighthouse, 50 m above the sea, the angle of depression of an incoming boat is 30°. How far is the boat from the lighthouse?
Options- A. 25 ?3 m
- B. 25 / ?3 m
- C. 50 ?3 m
- D. 50 / ?3 m Discuss
- 7. On the level ground, the angle of elevation of the top of the tower is 30°. On moving 20 m nearer, the angle of elevation is 60°. The height of the tower is :
Options- A. 20 ?3 m
- B. 10 ?3 m
- C. 10 ( ?3 - 1 ) m
- D. None of these Discuss
- 8. Angle of depression from the top of a lighthouse of two boats are 45° and 30° due east which are 60 m apart. The height of the light house is :
Options- A. 60 ?3
- B. 30 ( ?3 - 1 )
- C. 30 ( ?3 + 1 )
- D. None of these Discuss
- 9. If a flag staff of 6 m height placed on the top of a tower throws a shadow of 2 ?3 m along the ground, then the angle that the sun makes with the ground is :
Options- A. 60°
- B. 30°
- C. 45°
- D. None of these Discuss
- 10. The angle of elevation of the top of a TV tower from three points A, B, C in a straight line through the foot of the tower are ?, 2?, 3?, respectively. If AB = a, the height of the tower is :
Options- A. a tan ?
- B. a sin ?
- C. a sin 2?
- D. a sin 3? Discuss
Height and Distance problems
Search Results
Correct Answer: 10?3
Explanation:
Correct Answer: 100/ ?3
Explanation:
Correct Answer: None of these
Explanation:
Let OP be the tower of height h (say) and PQ the flag-staff of height a, such that
?OAP = ? and ?PAQ = ?
In ?OAP and ?OAQ
OA = OP cot ? = h cot?
and OA = OQ cot ( ? + ? ) = (h + a) cot ( ? + ? )
? h cot? = (h + a) cot ( ? + ? )
? h = a cot ( ? + ? ) / cot? - cot ( ? + ? )
Correct Answer: r Cosec ?/2 Sin ?
Explanation:
Let O be the centre of the balloon of radius r which subtend an angle ? at the eye of an observer at E .
If EA and EB are the tangents to the ballon,
then ? OEA = ? OEB = ?/2
In triangle ?OAE, Sin ?/2 = OA/OE
? OE = r cosec 1/2 ?
In ?OEL, height of the center of the balloon = h = OE sin ? = r Cosec ?/2 Sin ?.
Correct Answer: 1/?6
Explanation:
Let a be the length of a side of square plot ABCD and h, the height of the pole standing at D. Since elevations of P from A or C is 30° and that from B is ?,
? In triangle ? PCD, tan 30° = h/a
i.e h/a = 1/?3 .............. (1)
And in triangle ? PBD,
Since PD = h and BD = ?(AB2 + AD)2 = a?2.
Put the value of PD and BD , we will get
tan ? = PD/BD = h/(a?2)
put the value of h/a from equation (1)
tan ? = 1/?2 x 1/?3
tan ? = 1/?6
Correct Answer: 50 ?3 m
Explanation:
Correct Answer: 10 ?3 m
Explanation:
Correct Answer: 30 ( ?3 + 1 )
Explanation:
Correct Answer: 60°
Explanation:
Correct Answer: a sin 2?
Explanation:
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