Home
Class 12
MATHS
In a DeltaABC, if c = 2, A = 120^(@), a ...

In a `Delta`ABC, if c = 2, A = `120^(@)`, a = `sqrt(6)`, then what is C equal to ?

A

`30^(@)`

B

`45^(@)`

C

`60^(@)`

D

`75^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `c = 2, angle A = 120^(@)and a = sqrt(6)` in `Delta` ABC,
`therefore" "` By Sine rule, we have
`(a)/(sinA)=(c)/(sinC) rArr (sqrt(6))/(sin120^(@))=(2)/(sin C)`
`rArr sinC = (2xx sqrt(3))/(sqrt(6)xx2)=(1)/(sqrt(2))`
`rArr sin C = sin 45^(@) rArr angle C 45^(@)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY AND PROBABILIYT DISTRIBUTION

    NDA PREVIOUS YEARS|Exercise Multiple Choice Question|213 Videos

  • QUESTION PAPER 2021

    NDA PREVIOUS YEARS|Exercise MULTIPLE CHOICE QUESTIONS|120 Videos

Similar Questions

Explore conceptually related problems

In a DeltaABC , if c = 2, A=120^(@), a=sqrt(6) , then C=

In a triangle ABC, c = 2, A = 45^(@) , a = 2 sqrt(2) , than what is C equal to ?

In Delta ABC , if : A = 30^(@), C = 60^(@) , a =sqrt(2) then b and c

In a triangle ABC, if c=2 , A=120^(@) and a=c then what is angle C equal to

In Delta ABC , if : A = 60^(@), C = 60^(@) , c =sqrt(2) then a and b

In Delta ABC ,if a=2, B=120^(@),C=30^(@) then area of Delta ABC is

In a Delta ABC If A-B= 120^(@) ,R=8r then 8cos C=

In a triangle ABC, if a = 2, b = 3 and c=4 , then cos A is equal to

In a triangle ABC, A - B =120 ^(@) and R = 8r, then the value of cos C is

In a triangle ABC, /_B=90^(@) and /_C=2/_A , then what is AB^(2) equal to ?

NDA PREVIOUS YEARS-PROPERTIES OF TRIANGLE, INVERSE TRIGONOMETRIC FUNCTION-MCQ
  1. What is the value of "sin"^(-1)(4)/(5) + 2 "tan"^(-1)(1)/(3) ?

    Text Solution

    |

  2. ABC is a triangle in which BC = 10 cm, CA = 6 cm and AB = 8 cm. Which...

    Text Solution

    |

  3. In a DeltaABC, if c = 2, A = 120^(@), a = sqrt(6), then what is C equa...

    Text Solution

    |

  4. ABC is a right angles triangle at B. The hypotenuse AC is four times t...

    Text Solution

    |

  5. ABC is a right angles triangle at B. The hypotenuse AC is four times t...

    Text Solution

    |

  6. ABC is a triangle right-angled at B. The hypotenuse (AC) is four the p...

    Text Solution

    |

  7. ABC is a right angles triangle at B. The hypotenuse AC is four times t...

    Text Solution

    |

  8. Consider the following I. "cosec"^(-1)(-(2)/(sqrt(3)))=-(pi)/(3) I...

    Text Solution

    |

  9. If sin ("sin"^(-1)(1)/(5)+ "cos"^(-1)x)=1, then what is x equal to ?

    Text Solution

    |

  10. What is the principle value of sec^(-1)((2)/(sqrt(3))) ?

    Text Solution

    |

  11. In any triangle ABC, the sides are 6 cm, 10 cm and 14 cm. Then the tri...

    Text Solution

    |

  12. In a triangle ABC, if A = tan^(-1) 2 and B = tan^(-1) 3, then C is equ...

    Text Solution

    |

  13. If the sides of a triangle are in the ratio 2 : sqrt(6) : 1 + sqrt(3),...

    Text Solution

    |

  14. In a triangle ABC, A = 8, b = 10 and c = 12. What is the angle C equal...

    Text Solution

    |

  15. The sides a, b, c of a triangle ABC are in arithmetic progression and ...

    Text Solution

    |

  16. What is the value of cos {"cos"^(-1)(4)/(5)+ "cos"^(-1)(12)/(13)} ?

    Text Solution

    |

  17. In a triangle ABC if the angles A, B, C are in AP, then which one of t...

    Text Solution

    |

  18. If sin^(-1)1 + "sin"^(-1)(4)/(5)=sin^(-1)x, then what is x equal to?

    Text Solution

    |

  19. If two angles of a triangle are tan^1,2 and tan^1,3, what is the thir...

    Text Solution

    |

  20. What is the value of sec^(2)tan^(-1)((5)/(11))?

    Text Solution

    |