Home
Class 12
MATHS
A right triangle has perimeter of length...

A right triangle has perimeter of length 7 and hypotenuse of length `3.` If `theta` is the larger non-right angle in the triangle, then the value of `costheta equal`

A

`(sqrt6-sqrt2)/4`

B

`(4+sqrt2)/6`

C

`(4-sqrt2)/6`

D

`(4-sqrt2)/6`

Text Solution

Verified by Experts

The correct Answer is:
D
`"Perimeter "=7=3sintheta+3costheta+3," where " 45^@ltthetalt90^@`
`sintheta+costheta=4/3 ...(i)`
Since `(sintheta+costheta)^2+(sintheta-costheta)^2=2`, we have
`(sintheta-costheta)^2=2-(4/3)^2`

`rArrsintheta-costheta=sqrt2/3 ...(ii)`
From (i) and (ii),`costheta=(4-sqrt2)/6`
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

The circum radius of a right angled triangle is

Show that in a right angled triangle, the hypotenuse is the longest side.

Two sides of a triangle are of lengths 2a and 2b and contain an angle of 120^@ . If the angle opposites the sides 2a is theta , then the value of tantheta is equal to

IF the lengths of the side of triangle are 3,5 and 7, then the largest angle of the triangle is

To construct a right angled triangle whose one side and length of hypotenuse is given. In a right angled triangle, One angle has to be square [right angle/obtuse angle]

The lengths of the medians through acute angles of a right-angled triangle are 3 and 4. Find the area of the triangle.

An isosceles triangle has two equal sides of length 'a' and angle between them is prop . The area of the triangle is

The perimeter of a right-angled triangle is 60 cm and hypotenuse is 26 cm. Find the lengths of its other two sides.

Adhir has drawn a right-angled triangle whose length of hypotenuse is 6 cm more than the twice of the shortest side. If the length of the third side is 2 cm less than the length of the hypotenuse, then calculate the lengths of the three sides of the right-angled triangle drawn by Adhir.

The length of the hypotenuse of a right angled triangle is a Find the lenghts of its other sides , so that the area of the triangle is maximum.

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

    Text Solution

    |

  2. A circle is drawn in a sector of a larger circle of radius r , as show...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Which of the following is correct?

    Text Solution

    |

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

    Text Solution

    |

  7. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)......(2sin^2 18...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. The minimum value of sin^4theta+cos^4theta is

    Text Solution

    |

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

    Text Solution

    |