Home
Class 12
MATHS
Given that the side length of a rhombus ...

Given that the side length of a rhombus is the geometric mean of the length of its diagonals. The degree measure of the acute angle of the rhombus is `15^0` (b) `30^0` (c) `45^0` (d) `60^0`

A

`15^@`

B

`30^@`

C

`45^@`

D

`60^@`

Text Solution

Verified by Experts

The correct Answer is:
B
Area of rhomubs is given by
`2xx1/2x^2sintheta=(ab)/2` (Equating area of a rhombus)
Given `x^2=ab` (given)
`rArrsinteta=1/2`
`or theta=30^@`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

Given that the side length of a rhombus is the geometric mean of the length of its diagonals. The degree measure of the acute angle of the rhombus is (a)15(b) 30^(@) (c) 45^(0) (d) 60^(0)

Each side of a rhombus is 15 cm and the length of one its diagonals is 24 cm. The area of the rhombus is

The area of a rhombus is 480 cm^(2) and the length of one of its diagonals is 20 cm . The length of each side of the rhombus is

The length of each of the sides of a rhombus is given as 5 m and the length of one of its diagonals is 2.8 m Find the area of the rhombus.

The area of a rhombus is 216 cm^(2) and the length of one of its diagonals is 24 cm. How long is each side of the rhombus ?

The length of a side of rhombus is 5 meter and one of its diagonal is of length 8 meter. Theother diagonal is of length:

The length of a side of a rhombus is 10 m and one of its diagonal is 12 m. The length of the other diagonal is :

CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. A circle is drawn in a sectore of a larger circle of radius r, as show...

    Text Solution

    |

  2. A right triangle has perimeter of length 7 and hypotenuse of length 3....

    Text Solution

    |

  3. Given that the side length of a rhombus is the geometric mean of the ...

    Text Solution

    |

  4. Which of the following is correct?

    Text Solution

    |

  5. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |

  6. if sin^2theta=(x^2+y^2+1)/(2x) then x must be

    Text Solution

    |

  7. sec^2 x=(4xy)/(x+y)^2 is true if and only if

    Text Solution

    |

  8. If sintheta1+sintheta2+sintheta3=3," then "costheta1+costheta2+costhet...

    Text Solution

    |

  9. If sinx+siny+sinz+sinw=-4" then the value of "sin^400x+sin^300y+sin^20...

    Text Solution

    |

  10. The minimum value of the expression sin alpha + sin beta+ sin gamma, ...

    Text Solution

    |

  11. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

    Text Solution

    |

  12. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)(2sin^2 180^0-1)...

    Text Solution

    |

  13. If sinA=sin^2B and 2cos^2A=3cos^2B then the triangle ABC is

    Text Solution

    |

  14. If sintheta+costheta=1/5and 0lethetaltpi" then "tantheta is

    Text Solution

    |

  15. If piltalphalt(3pi)/2lt" then "sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1...

    Text Solution

    |

  16. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

    Text Solution

    |

  17. The least value of 2sin^2theta+3cos^2theta is

    Text Solution

    |

  18. The greatest value of sin^4theta+cos^4theta is

    Text Solution

    |

  19. If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] ...

    Text Solution

    |

  20. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

    Text Solution

    |