Home
Class 12
MATHS
If b=3,c=4,a n dB=pi/3, then find the nu...

If `b=3,c=4,a n dB=pi/3,` then find the number of triangles that can be constructed.

Text Solution

Verified by Experts

We have,
`(sin B)/(b) = (sin C)/(c) " or " (sin (pi//3))/(3) = (sin C)/(4)`
or `sinC = (2)/(sqrt3) gt 1`, which is not possible
Hence, no triangle is possible
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

If A=30^0, a=7,and b=8 in A B C , then find the number of triangles that can be constructed.

The sides AB, BC and CA of a triangle ABC have 3,4 and 5 interior points respectively on them . the number of triangle that can be constructed using these interior points as vertices , is

If a ,b ,c in {1,2,3,4,5,6,} find the number of ways a, b, c can be selected if f(x)=x^(3)+a x^2+b x+c is an increasing function.

The length of three sides of the tingles are given. Identify the cases where, the triangles can be constructed and construct those triangles, and give reasons for the cases where the triangle cannot be constructed: 9cm, 4cm, 4cm.

The length of three sides of the tingles are given. Identify the cases where, the triangles can be constructed and construct those triangles, and give reasons for the cases where the triangle cannot be constructed: 4cm, 5cm & 7cm.

In a triangle ABC, (a)/(b) = (2)/(3) and sec^(2) A = (8)/(5) . Find the number of triangle satisfying these conditions

If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value of tanB

(i) If a:b:c= 2:3:4 and s=27 inches, find the area of the triangle ABC. (ii) If in a triangle ABC, a=6, b=3 and cos(A-B) =4/5 then find its area.

Let A-=(6,7),B-=(2,3)a n dC-=(-2,1) be the vertices of a triangle. Find the point P in the interior of the triangle such that P B C is an equilateral triangle.

If characteristic of three numbers a, b and c and 5, -3 and 2, respectively, then find the maximum number of digits in N = abc.

CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. In triangle A B C ,a : b : c=4:5: 6. The ratio of the radius of the ci...

    Text Solution

    |

  2. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

    Text Solution

    |

  3. If b=3,c=4,a n dB=pi/3, then find the number of triangles that can be ...

    Text Solution

    |

  4. If A=30^0, a=7,and b=8 in A B C , then find the number of triangles t...

    Text Solution

    |

  5. If in triangle ABC, (a=(1+sqrt(3))c m ,b=2c m ,a n d/C=60^0 , then fin...

    Text Solution

    |

  6. In A B C , sides b , c and angle B are given such that a has two val...

    Text Solution

    |

  7. In A B C ,a , ca n dA are given and b1,b2 are two values of the third...

    Text Solution

    |

  8. O is the circumcenter of A B Ca n dR1, R2, R3 are respectively, the r...

    Text Solution

    |

  9. In A B C ,C=60^0a n dB=45^0dot Line joining vertex A of triangle and ...

    Text Solution

    |

  10. The diameters of the circumcirle of triangle ABC drawn from A,B and C ...

    Text Solution

    |

  11. Find the lengths of chords of the circumcircle of triangle ABC, made b...

    Text Solution

    |

  12. Let A B C be a triangle with /B=90^0 . Let AD be the bisector of /A wi...

    Text Solution

    |

  13. If the distances of the vertices of a triangle =ABC from the points of...

    Text Solution

    |

  14. If x , ya n dz are the distances of incenter from the vertices of the ...

    Text Solution

    |

  15. prove that cosA +cosB+cosC=1+r/R.

    Text Solution

    |

  16. Prove that ("a c o s"A+b cosB+c cosC)/(a+b+c)=r/Rdot

    Text Solution

    |

  17. Incircle of A B C touches the sides BC, CA and AB at D, E and F, resp...

    Text Solution

    |

  18. In an acute angled triangle A B C , a semicircle with radius ra is con...

    Text Solution

    |

  19. Let the incircle with center I of A B C touch sides BC, CA and AB at ...

    Text Solution

    |

  20. In A B C , the bisector of the angle A meets the side BC at D andthe ...

    Text Solution

    |