Home
Class 12
MATHS
Let ABC be a triangle such that angleACB...

Let ABC be a triangle such that `angleACB=pi/6` and let a , b and c denote the lengths of the side opposite to A ,B and C respectively. The value of x for which `a=x^(2)+x+1,b=x^(2)-1` and `c=2x+1` is

A

`-(2+sqrt(3))`

B

`1+sqrt(3)`

C

`2+sqrt(3)`

D

`4sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise Evaluation Test|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise Critical Thinking|88 Videos

  • THREE DIMENSIONAL GEOMETRY

    TARGET PUBLICATION|Exercise Evaluation Test|9 Videos

  • VECTORS

    TARGET PUBLICATION|Exercise Evaluation Test|18 Videos

Similar Questions

Explore conceptually related problems

Let ABC be a triangle such that /_ABC=(pi)/(6) and let a,b and c denote the lengths of the sides opposite to A,B and C respectively. The value(s) of x for which a=x^(2)+x+1,b=x^(2)-1 and c=2x+1 is /are(a)-(2+sqrt(3))(b)1+sqrt(3)(c)2+sqrt(3) (d) 4qsrt3

Let ABC be a triangle such that /_ACB=(pi)/(6) and let a,b and c denote the lengths of the side opposite to A,B, and C respectively.The value(s) of x for which a=x^(2)+x+1,b=x^(2)-1, and c=2x+1 is(are) -(2+sqrt(3))( b) 1+sqrt(3)2+sqrt(3)(d)4sqrt(3)

Consider a triangle ABC and let a,b and c denote the lengths of the sides opposite to vertices A,B and C respectively.If a=1,b=3 and C=60^(@), the sin^(2)B is equal to

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a)/(c) sin 2C + (c)/(a) sin 2A is

If the angle A,B and C of a triangle are in an arithmetic propression and if a,b and c denote the lengths of the sides opposite to A,B and C respectively,then the value of the expression (a)/(c)sin2C+(c)/(a)sin2A is (1)/(2)(b)(sqrt(3))/(2) (c) 1(d) sqrt(3)

Consider a triangle ABC and let a , b , and c denote the lengths of the sides opposite to vertices A , B and C respectively. suppose a = 6 , b = 10 and the area of the triangle is 15sqrt3 . If angleACB is obtuse and if r denotes the radius of the in circle of the triangle , then r^(2) is equal to

Consider a triangle ABC and let a,b and c denote the lengths of the sides opposite to vertices A,B, and C, respectively.Suppose a=6,b=10, and the area of triangle is 15sqrt(3.) If /_ACB is obtuse and if r denotes the radius of the incircle of the triangle,then the value of r^(2) is

TARGET PUBLICATION-TRIGONOMETRIC FUNCTIONS -Competitive Thinking
  1. If the sides of the triangle ABC are p,q and sqrt(p^(2)+ pq+q^(2)), th...

    Text Solution

    |

  2. If the line segment joining the points A(a,b) and B(c,d) subtends an a...

    Text Solution

    |

  3. Let ABC be a triangle such that angleACB=pi/6 and let a , b and c deno...

    Text Solution

    |

  4. If two adjacent sides of a cyclic quadrilateral aré 2 and 5 and the an...

    Text Solution

    |

  5. In triangle ABC, if A = 2B, and the sides opposite to the angles A, B,...

    Text Solution

    |

  6. In triangleABC, (b+c)cosA+(c+a)cosB+(a+b)cosC=

    Text Solution

    |

  7. In DeltaABC,cosecA(sinBcosC+cosBsinC)=

    Text Solution

    |

  8. IN triangleABC, (cosC+cosA)/(c+a)+(cosB)/(b)=

    Text Solution

    |

  9. In DeltaABC, with usual notations, if a,b,c are in AP then acos^(2)((C...

    Text Solution

    |

  10. In a DeltaABC, if 2s=a+b+cand(s-b)(s-c)=xsin^(2).(A)/(2), then x =

    Text Solution

    |

  11. In triangle ABC, sin((A)/(2))sin((C)/(2))=sin((B)/(2)) and '2s' is the...

    Text Solution

    |

  12. In triangleABC, if a=18, b=24, c=30, then cos((A)/(2))=

    Text Solution

    |

  13. In DeltaABC,(a-b)^(2)cos^(2).(C)/(2)+(a+b)^(2)sin^(2).(C)/(2)=

    Text Solution

    |

  14. If a, b, c are in A.P then cot(A/2),cot(B/2),cot(C/2) are in

    Text Solution

    |

  15. In DeltaABC,tan.(A)/(2)+tan.(B)/(2)=

    Text Solution

    |

  16. In DeltaABC,(cot.(A)/(2)+cot.(B)/(2))(asin^(2).(B)/(2)+bsin^(2).(A)/(2...

    Text Solution

    |

  17. If the sides of a triangle are in A.P., then the cotangent of its half...

    Text Solution

    |

  18. If c^(2)=a^(2) +b^(2), then 4s(s-a)(s-b)(s-c) is equal to

    Text Solution

    |

  19. The area of an isosceles triangle is 9 cm^(2). If the equal sides are ...

    Text Solution

    |

  20. The area of the triangle ABC,in which a=1,b=2angleC=60^(@) is

    Text Solution

    |