Home
Class 12
MATHS
In a triangle A B CifB C=(3)^(1/2) and A...

In a triangle `A B CifB C=(3)^(1/2) and A C=2,` then what is the maximum possible value of angle `A ?`

Text Solution

Verified by Experts

Using Sine Rule, `(1)/(sin A) = (2)/(sin B)`
or `sin A = (sin B)/(2)`

`rArr` Maximum valur of `sin A " is " (1)/(2)`
Hence, `A = (pi)/(6)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.2|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

In a triangle A B CifB C=1 and AC=2, then what is the maximum possible value of angle A ?

In a triangle ABC, if (sqrt3-1)a = 2b, A = 3B , then /_C is

In triangle ABC, if (a+b+c)(b+c-a) = 3bc, state which of the following is the value of the angle A?

In triangle A B C , if angle is 90^0 and the area of triangle is 30 sqdot units, then the minimum possible value of the hypotenuse c

In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of 3 (b) 6 (c) 9 (d) none of these

In a triangle ABC if b+c=3a then find the value of cot(B/2)cot(C/2)

In a triangle A B C ,/_A=60^0a n db : c=(sqrt(3)+1):2, then find the value of (/_B-/_C)dot

In triangle A B C ,2a csin(1/2(A-B+C)) is equal to

If in a triangle ABC, cos^(2)A + cos^(2)B + cos^(2)C =1 , then show that the triangle is right angled.

CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. If an a triangle A B C , a=3b and B-A=90^0, then find the value of tan...

    Text Solution

    |

  2. In a triangle A B CifB C=(3)^(1/2) and A C=2, then what is the maximum...

    Text Solution

    |

  3. The perimeter of a triangle ABC is saix times the arithmetic mean of ...

    Text Solution

    |

  4. If A=75^0,b=45^0, then prove that b+csqrt(2)=2a

    Text Solution

    |

  5. If the base angles of triangle are (22)/(12)a n d112 1/2^0 , then prov...

    Text Solution

    |

  6. If a^2, b^2,c^2 are in A.P., then prove that tanA ,tanB ,tanC are in H...

    Text Solution

    |

  7. Prove that (a^2sin(B-C))/(sinB+sinC)+(b^2"sin"(C-A))/(sinC+sinA)+(c^2"...

    Text Solution

    |

  8. in triangleABC if (a^2+b^2)/(a^2-b^2)=sin(A+B)/sin(A-B) then prove th...

    Text Solution

    |

  9. ABCD is a trapezium such that AB,DC.are parallel and BC is perpendicul...

    Text Solution

    |

  10. In a "DeltaA B C","\ "/"C"=60"\ "&\ /A=75. If D is a point on A C such...

    Text Solution

    |

  11. In a scalene triangle A B C ,D is a point on the side A B such that C ...

    Text Solution

    |

  12. In a triangle A B C ,/A=60^0a n db : c=(sqrt(3)+1):2, then find the va...

    Text Solution

    |

  13. If the median AD of triangle ABC makes an angle pi/4 with the side BC,...

    Text Solution

    |

  14. The base of a triangle is divided into three equal parts. If t1, t2,t3...

    Text Solution

    |

  15. In A B C , prove that (a-b)^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

    Text Solution

    |

  16. In A B C ,= if (a+b+c)(a-b+c)=3a c , then find /Bdot

    Text Solution

    |

  17. If a=sqrt(3),b=1/2(sqrt(6)+sqrt(2))dot and c=2, then find /A

    Text Solution

    |

  18. The sides of a triangle are x^2+x+1,2x+1,a n dx^2-1 . Prove that the g...

    Text Solution

    |

  19. If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in ...

    Text Solution

    |

  20. Let a, b and c be the three sides of a triangle, then prove that the e...

    Text Solution

    |