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 PUBLICATION|Exercise Multiple Correct Answers Type|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.14|1 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 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) 15^0 (b) 30^0 (c) 45^0 (d) 60^0

If the lengths of the diagonals of a rhombus be 18cm and 24 cm. Then find the length of its sides.

If the hypotenuse of a right-angled triangle is four times the length of the perpendicular drawn from the opposite vertex to it, then the difference of the two acute angles will be 60^0 (b) 15^0 (c) 75^0 (d) 30^0

If the length of one of the diagonals of a rhombus with sides 13cm be 10cm, then find the length of its other diagonal.

What is the length of the other diagonal of a rhombus , if one its diagonal is 12 cm and the sides of it is 10 cm.

If the two sides of rhombus are x+2y+2=0 and 2x+y-3=0, then find the slope of the longer diagonal.

Two sides of a rhombus lying in the first quadrant are given by 3x-4y=0a n d12 x-5y=0 . If the length of the longer diagonal is 12, then find the equations of the other two sides of the rhombus.

L_1a n dL_2 are two lines. If the reflection of L_1onL_2 and the reflection of L_2 on L_1 coincide, then the angle between the lines is (a) 30^0 (b) 60^0 45^0 (d) 90^0

Prove that the points (0,0),(0,10),(8,16)and (8,6)are the vertices of a rhombus , find the area of the rhombus. Show also that the diogonal of the rhombus intersect at right angle

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. A circle is drawn in a sector 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 -3 (b) -2 (c) 1 (d)...

    Text Solution

    |

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

    Text Solution

    |

  8. If sinx+siny+sinz=3," then "cosx+cosy+cosz is equal to

    Text Solution

    |

  9. If sinx+sin y+sinz+sinw=-4, then the value of sin^(400)x+sin^(300)y+si...

    Text Solution

    |

  10. Prove that, SinA/(1-cosA) =CosecA+cotA

    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 18...

    Text Solution

    |

  13. If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right an...

    Text Solution

    |

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

    Text Solution

    |

  15. If π<α<(3π)/2 then sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/...

    Text Solution

    |

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

    Text Solution

    |

  17. The least value of 3sin^2theta+4cos^2theta is

    Text Solution

    |

  18. The minimum 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

    |