Home
Class 12
MATHS
The distance between the two parallel li...

The distance between the two parallel lines is 1 unit. A point A is chosen to lie between the lines at a distance 'd' from one of them Triangle ABC is equilateral with B on one line and C on the other parallel line. The length of the side of the equilateral triangle is

A

`(2)/(3) sqrt(d^(2)+d+1)`

B

`2sqrt((d^(2)-d+1)/(3))`

C

`2sqrt(d^(2)-d+1)`

D

`sqrt(d^(2)-d+1)`

Text Solution

Verified by Experts

The correct Answer is:
B
From figure ltbr. `x cos (theta+30^(@))=d`
and `x sin theta=1-d`
Dividing `sqrt(3) cot theta=(1+d)/(1-d)`
squaring Eq. ii and putting the value of `cos theta` , we get
`x^(2)=(1)/(3)(4d^(2)-4d+4)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

The distance between the parallel lines y=x +a, y =x+ b is

The distance between two parallel lines is unity. A point P lies between the lines at a distance a from one of them. Find the length of a side of an equilateral triangle PQR vertex Q of which lies on one of the parallel lines and vertex R lies on the other line.

The distance between two parallel lines can be taken out by the formula

Shortest distance between two parallel lines in vector + cartesian form

ABC is an equilateral triangle such that the vertices B and C lie on two parallel at a distance 6. If A lies between the parallel lines at a distance 4 from one of them then the length of a side of the equilateral triangle.

A point P is inside an equilateral triangle if the distance of P from sides 8,10,12 then the length of the side of the triangle is

The equation of the lines through the origin which form two of the sides of the equilateral triangle having x=2 as the third side is

An equilateral triangle ABC has its centroid at the origin and the base BC lies along the line x+y=1. Area of the equilateral Delta ABC is

If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.

If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. In a right angled triangle the hypotenuse is 2sqrt2 times the perpendi...

    Text Solution

    |

  2. A circular ring of radius 3cm hangs horizontally form a point 4cm v...

    Text Solution

    |

  3. The distance between the two parallel lines is 1 unit. A point A is ch...

    Text Solution

    |

  4. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then asqrt(1-a^2)+bsqrt(1-b^2)+cs...

    Text Solution

    |

  5. If A+B+C=3pi/2. Then cos 2A +cos 2B+cos2C is equal to

    Text Solution

    |

  6. If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta), then

    Text Solution

    |

  7. In any triangle A B C ,sin^2A-sin^2B+sin^2C is always equal to 2sinAsi...

    Text Solution

    |

  8. The value of sum(r=0)^10cos^3((rpi)/3) is

    Text Solution

    |

  9. In triangle ABC,(sinA+sinB+sinC)/(sinA+sinB-sinC) is equal to

    Text Solution

    |

  10. (sin2A+sin2B+sin2C)/(sinA+sinB +sinC) is equal to

    Text Solution

    |

  11. If cos^(2)A+cos^(2)B+cos^(2)C=1, then triangle ABC is

    Text Solution

    |

  12. In a triangle tan A+ tan B + tan C=6 and tan A tan B= 2, then the valu...

    Text Solution

    |

  13. If cos x+cos y-cos(x+y)=(3)/(2), then

    Text Solution

    |

  14. If a sin x+b cos(x+theta)+b cos(x-theta)=d, then the minimum value of ...

    Text Solution

    |

  15. If u=sqrt(a^2cos^2theta+b^2sin^2theta)+sqrt(a^2sin^2theta+b^2cos^2thet...

    Text Solution

    |

  16. If tanx =n tany , n in R^+ then the maximum value of sec^2(x-y) is

    Text Solution

    |

  17. If 0lt=xlt=pi/3 then range of f(x)=sec(pi/6-x)+sec(pi/6+x) is (4/(sqrt...

    Text Solution

    |

  18. The maximum value of cos xsin x+sqrt(sin^(2)x+sin^(2)((pi)/(6))} is

    Text Solution

    |

  19. If alpha,beta,gamma are ccute angles and costheta=sinbeta//sinalpha,co...

    Text Solution

    |

  20. sum(n=1)^ootan(theta/(2^n))/(2^(n-1)cos(theta/(2^(n-1))))

    Text Solution

    |