446. The angle of elevation of a ladder leaning against a house is 60° and the foot of the ladder is 6.5 metres from the house. The length of the ladder is

1. 1. 	13	m
      	√3

   
   
   

   2. 13 metres

   
   
   

   3. 15 metres

   
   
   

   4. 3.25 metres

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   AB = house, AC = ladder
   In ∆ABC,
   

   cos 60° =	BC
   	AC

   
   

   ⇒	1	=	6.5
   	2		AC

   
   ⇒ AC = 2 × 6.5 = 13 metre

   Correct Option: B

   
   AB = house, AC = ladder
   In ∆ABC,
   

   cos 60° =	BC
   	AC

   
   

   ⇒	1	=	6.5
   	2		AC

   
   ⇒ AC = 2 × 6.5 = 13 metre

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447. From a point 20 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The height of the tower is

1. 1. 10 √3 m

   
   
   

   2. 20 √3 m

   
   
   

   3. 	10	m
      	√3

   
   
   

   4. 	20	m
      	√3

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   AB = Tower, BC = 20 metre
   In ∆ ABC.
   

   tan 30° =	AB
   	BC

   
   

   ⇒	1	=	AB
   	√3		20

   
   

   ⇒ AB =	20	metre
   	√3

   Correct Option: D

   
   AB = Tower, BC = 20 metre
   In ∆ ABC.
   

   tan 30° =	AB
   	BC

   
   

   ⇒	1	=	AB
   	√3		20

   
   

   ⇒ AB =	20	metre
   	√3

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448. The angle of elevation of the top of a vertical tower situated perpendicularly on a plane is observed as 60° from a point P on the same plane. From another point Q, 10 m vertically above the point P, the angle of depression of the foot of the tower is 30°. The height of the tower is

1. 1. 15 m

   
   
   

   2. 30 m

   
   
   

   3. 20 m

   
   
   

   4. 25 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   AB = Tower = h metre
   PQ = 10 metre
   ∠ APB = 60°,
   ∠ CQB = ∠ QBP = 30°
   In ∆ PBQ,
   

   tan 30° =	PQ
   	PB

   
   

   ⇒	1	=	10
   	√3		PB

   
   ⇒ PB = 10 √3 metre
   In ∆ APB,
   

   tan 60° =	AB
   	PB

   
   

   ⇒ √3 =	h
   	10√3

   
   ⇒ h = √3 × 10 √3 = 30 metre

   Correct Option: B

   
   AB = Tower = h metre
   PQ = 10 metre
   ∠ APB = 60°,
   ∠ CQB = ∠ QBP = 30°
   In ∆ PBQ,
   

   tan 30° =	PQ
   	PB

   
   

   ⇒	1	=	10
   	√3		PB

   
   ⇒ PB = 10 √3 metre
   In ∆ APB,
   

   tan 60° =	AB
   	PB

   
   

   ⇒ √3 =	h
   	10√3

   
   ⇒ h = √3 × 10 √3 = 30 metre

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449. From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff.
     (Take √3 = 1.732)

1. 1. 10 (√3 + 2) m

   
   
   

   2. 10 (√3 + 1) m

   
   
   

   3. 10 √3 m

   
   
   

   4. 7.32 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   AC = Flag
   AB = building = 10 metre
   ∠ APB = 30°; ∠ CPB = 45°
   In ∆ APB,
   

   tan 30° =	AB
   	PB

   
   

   ⇒	1	=	10
   	√3		PB

   
   ⇒ PB = 10 √3 metre
   In ∆ PBC,
   

   tan 45° =	BC
   	PB

   
   

   ⇒ 1 =	AB + AC
   	PB

   
   ⇒ PB = AB + AC
   ⇒ 10 √3 = 10 + AC
   ⇒ AC = 10 √3 – 10
   = 10 ( √3 –1) metre
   = 10 (1.732 – 1) metre
   = 10 × 0. 732 = 7.32 metre

   Correct Option: D

   
   AC = Flag
   AB = building = 10 metre
   ∠ APB = 30°; ∠ CPB = 45°
   In ∆ APB,
   

   tan 30° =	AB
   	PB

   
   

   ⇒	1	=	10
   	√3		PB

   
   ⇒ PB = 10 √3 metre
   In ∆ PBC,
   

   tan 45° =	BC
   	PB

   
   

   ⇒ 1 =	AB + AC
   	PB

   
   ⇒ PB = AB + AC
   ⇒ 10 √3 = 10 + AC
   ⇒ AC = 10 √3 – 10
   = 10 ( √3 –1) metre
   = 10 (1.732 – 1) metre
   = 10 × 0. 732 = 7.32 metre

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450. If in a triangle ABC, sin A = cos B, then the value of cos C is
     

1. 1. √3

      2

      
      

   
   
   

   2. 0
      

   
   
   

   3. 1
      

   
   
   

   4. 1

      √2

   
   
   

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1. View Hint View Answer Discuss in Forum

   sin A = cos B
   ⇒ sin A = sin (90° – B)
   ⇒ A = 90° – B
   ⇒ A + B = 90°
   ∴ ∠C = 90°
   ∴ cos C = cos 90° = 0

   Correct Option: B

   sin A = cos B
   ⇒ sin A = sin (90° – B)
   ⇒ A = 90° – B
   ⇒ A + B = 90°
   ∴ ∠C = 90°
   ∴ cos C = cos 90° = 0

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