Question

Neeraj who belongs to a small town in Maharashtra was coming to a big city for the first time. As he was driving past the Mumbai airport road along with his family, he observed a big billboard of length 6 m and width 3 m. Further, ∠DQA = 30° and ∠APB = 30°. D 30° 30° P B A Q C 41. The length AP is :
(a) 6 m
(b) 6 3 m
(c) 12 m
(d) 12 3m

42. The length BP is:
(a) 6 m
(b) 12 m
(c) 6 3 m
(d) 12 3 m

43. Ratio of sin ∠APB : sin ∠AQD is:
(a) 1 : 2
(b) 1 : 3
(c) 3 : 1
(d) 1 : 1

44. The value of sin 60° cos 30° + sin 30° cos 60° is:
(a) 1
(b) 0
(c) –1
(d) 4 1

45. The length of (AP + AQ) is:
(a) 6^ h 3 1 + m
(b) 18 m
(c) 36 m
(d) 12^ h 3 1 + m​

Answer 1

Answer:

41. (c) 12 m

42. (c) 6√3 m

43. (d) 1 : 1

44. (a) 1

45. (b) 18 m

Explanation:

AB = CD = 6 m

BC = AD = 3 m

∠DQA = 30°

∠APB = 30°

41. sin 30° = ½

AB/AP = ½

6/AP = ½

(c) AP = 12 m

42. cos 30° = √3/2

BP/AP = √3/2

BP/12 = √3/2

(c) BP = 6√3 m

43. sin ∠APB = ½

sin ∠AQD = ½

(d) So, sin ∠APB : sin ∠AQD = 1 : 1

44. sin 60° × cos 30° = √3/2 × √3/2 = ¾

sin 30° × cos 60° = ½ × ½ = ¼

(a) So, sin 60° × cos 30° + sin 30° × cos 60°

= ¾ + ¼

= 1

45. AP = 12 m

AD/AQ = ½

3/AQ = ½

AQ = 6 m

(b) So, (AP + AQ) = 12 + 6 = 18 m