Home
Class 11
MATHS
If the base angles of triangle are ((22)...

If the base angles of triangle are `((22)/(12))^@` and `(112 1/2)^@` , then prove that the altitude of the triangle is equal to `1/2` of its base.

Text Solution

Verified by Experts

We can create a diagram with the given details.
Please refer to video to see the diagram.
`/_BAC = 180-112.5-22.5 = 45^@`
`/_ACL = 180-112.5 = 67.5^@`
Now, in `Delta ABC`,
From sine law,
`(BC)/(sin45^@) =( AC)/(sin22.5^@)`
`=>AC = (BC sin22.5^@)/sin45^@`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

The base angles of a triangle are (22 (1)/(2))^(@)and (112 (1)/(2))^(@). If b is the base and h is the height of the triangle then-

if the lengths of sides of a triangle be 1-2x, (x^2-x+1 and (x^2-1) then show that the greatest angle of the triangle is 120^@

The sides of a triangle ABC are (x^(2) + x +1),(2x+1) and (x^(2)-1) . Find the greatest angle of the triangle.

if two angles of a triangle are tan ^(-1)""(1)/(2) and tan^(-1) ""(1)/(3) , then find the third angle .

if two angles of a triangle are cot ^(-1)""(1)/(2) and cot ^(-1)""(1)/(3) then find the third angle .

If the angles of a triangle are in ratio 1 : 1 : 2, then the ratio of the sides of the triangle is

If the equation of base of an equilateral triangle is 2x-y=1 and the vertex is (-1,2), then the length of the sides of the triangle is

In a triangle of base a, the ratio of the other sides is r(lt1). Show that the attitude of the triangle is less than or equal to (ar)/(1-r^2.

If the equation of the base of an equilateral triangle is 2x - y=1 and the vertex is (-1,2), then the length of a side of the triangle is-

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If an a triangle A B C , b=3 c, a n d C-B=90^0, then find the value o...

    Text Solution

    |

  2. The real roots of the equation cos^7x+sin^4x=1 in the interval (-pi,pi...

    Text Solution

    |

  3. If the base angles of triangle are ((22)/(12))^@ and (112 1/2)^@ , th...

    Text Solution

    |

  4. The general solution of the trigonometric equation sinx+cosx=1 is give...

    Text Solution

    |

  5. Prove that: (sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(co...

    Text Solution

    |

  6. The equation 2cos^2 (x/2)sin^2x=x^2+x^(-2);0

    Text Solution

    |

  7. The perimeter of a triangle ABC is saix times the arithmetic mean of ...

    Text Solution

    |

  8. One of the general solutions of 4sinthetasin2thetasin4theta=sin3theta ...

    Text Solution

    |

  9. If A=75^@,B=45^@, then prove that b+csqrt(2)=2a

    Text Solution

    |

  10. The general solution of the equation 8cosxcos2xcos4x=(sin6x)/(sin x) ...

    Text Solution

    |

  11. in triangleABC if (a^2+b^2)/(a^2-b^2)=sin(A+B)/sin(A-B) then prove th...

    Text Solution

    |

  12. (sin^3theta-cos^3theta)/(sintheta-costheta)-(costheta)/(sqrt(1+cot^2th...

    Text Solution

    |

  13. ABCD is a trapezium such that AB,DC.are parallel and BC is perpendicul...

    Text Solution

    |

  14. For 0ltx ,yltpi,the number of ordered pairs (x, y) satisfying system e...

    Text Solution

    |

  15. In ABC with usual notations, if r=1,r1=7 and R=3, the (a) ABC is equil...

    Text Solution

    |

  16. The least positive solution of cot(pi/(3sqrt3) sin2x)=sqrt3

    Text Solution

    |

  17. If 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,then tan A is equal

    Text Solution

    |

  18. In Delta ABC, a^(2)(s-a)+b^(2)(s-b)+c^(2)(s-c)=

    Text Solution

    |

  19. The minimum value of ((3sin x-4cosx-10)(3sinx+4cosx-10)) is

    Text Solution

    |

  20. The number of real roots of the equation cos e ctheta+sectheta-sqrt(15...

    Text Solution

    |