Home
Class 12
MATHS
Consider a triangular plot ABC with side...

Consider a triangular plot ABC with sides AB = 7 m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is:

A

`2/3 sqrt21`

B

`2 sqrt21`

C

`7 sqrt3`

D

`3/2 sqrt21`

Text Solution

Verified by Experts

The correct Answer is:
B

`AB^2 + BC^2 + 2 (BD^2 + CD^2)`
` 49 + 25 = 2 (BD^2 + 9)`
` BD^2 = 28`
`BD = 2 sqrt7`
` tan60^@ = (DP)/(2sqrt7)`
`DP = 2 sqrt(21)`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 18

    VMC MODULES ENGLISH|Exercise MATHEMATICS - SECTION 2|5 Videos

  • JEE MAIN REVISION TEST - 22 JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the mid-point D of AC subtends an angle 30^(@) at B. The height (in m) of the lamp-post is

Construct Delta ABC with sides AB = 7 cm, BC = 5 cm, CA = 6 cm.

A lamp post is situated at the middle point M of the side AC of a triangular plot of ABC with B C=7m ,\ C A=8\ a n d\ A B=9mdot Lamp post subtends an angle of 15^0 at the point B. determine the height of the lamp post.

Construct a triangle ABC in which AC=5cm, BC= 7 cm and AB= 6cm. Mark D, the mid-point of AB

In Delta ABC, AB = 5cm , BC = 8 cm and CA = 7cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.

ABC is a triangular park with AB = AC = 100 m. A block tower is situated at the midpoint of BC.The angles of elevation of the top of the tower at A and B are cot^-1(3.2) and cosec^-1(2.6) respectively.The height of the tower is:

Sides of triangleABC, AB=7 cm, BC=5cm, CA=6cm . A pole is stand at mid point of side AC . Angle of elevation of pole from vertex B is 30^@ , find height of pole (a) sqrt7/sqrt3 (b) (2sqrt7)/sqrt3 (c) 2sqrt21 (d) 2sqrt7

From the top of a building A B , 60 m high, the angles of depression of the top and bottom of a vertical lamp post C D are observed to be 30o and 60o respectively. Find the height of the lamp post.

In a triangle ABC the sides BC=5, CA=4 and AB=3 . If A(0,0) and the internal bisector of angle A meets BC in D (12/7,12/7) then incenter of triangle ABC is

A triangle ABC has angle B = angle C . Prove that : (i) the perpendiculars from the mid-point of BC to AB and AC are equal. (ii) the perpendicular from B and C to the opposite sides are equal.

VMC MODULES ENGLISH-JEE MAIN REVISION TEST - 19-MATHEMATICS
  1. Let I=undersetaoversetbint(x^4-2x^2)dx. If is minimum, then the ordere...

    Text Solution

    |

  2. If a circle C passing through the point (4, 0) touches the circle x^(2...

    Text Solution

    |

  3. Let veca = 2hati+lambda1 hatj+3hatk, vec(b)=4hati+(3-lambda2) hatj+6ha...

    Text Solution

    |

  4. If the area enclosed between the curves y=kx^2 and x=ky^2, where kgt0,...

    Text Solution

    |

  5. An unbiased coin is tossed. If the outcome is a head then a pair of un...

    Text Solution

    |

  6. Consider a triangular plot ABC with sides AB = 7 m, BC = 5m and CA = 6...

    Text Solution

    |

  7. The mean of five observations is 5 and their variance is 9.20. If thre...

    Text Solution

    |

  8. Let f : RtoR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)...

    Text Solution

    |

  9. If the line 5x + 12y - 60 = 0 intersects the x-axis at the point A an...

    Text Solution

    |

  10. Let A be a point on the line vecr = (1- 5 mu) hati + (3mu - 1) hatj + ...

    Text Solution

    |

  11. The equation of a tangent to the hyperbola 9x^2 - 12y^2 = 144 paralle...

    Text Solution

    |

  12. Consider the statement: "P(n): n^(2)-n+41 is prime". Then which one of...

    Text Solution

    |

  13. The sum of all values of theta in (0,(pi)/(2)) satisfying sin^(2)2thet...

    Text Solution

    |

  14. Let nge2 be a natural number and 0ltthetaltpi//2. Then int((sin^ntheta...

    Text Solution

    |

  15. The condition that the parabolas y^2=4c(x-d) and y^2=4ax have a common...

    Text Solution

    |

  16. If underset(i=1)overset(20)Sigma((.^(20)C(i-1))/(.^(20)C(i)+.^(20)C(i-...

    Text Solution

    |

  17. In a class of 140 students numbered 1 to 140, all even numbered studen...

    Text Solution

    |

  18. The sum of all two digit positive numbers which when divided by 7 yiel...

    Text Solution

    |

  19. If the system fo equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + a...

    Text Solution

    |

  20. Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne...

    Text Solution

    |