Maths-
General
Easy

Question

In the triangle ABC, angle B equals fraction numerator pi over denominator 3 end fraction blank a n d blank angle C equals fraction numerator pi over denominator 4 end fraction blank. Let D divide BC internally in the ratio 1:3. Thenfraction numerator s i n invisible function application angle B A D over denominator s i n invisible function application angle C A D end fraction equals

  1. fraction numerator 1 over denominator square root of 6 end fraction    
  2. fraction numerator 1 over denominator 3 end fraction    
  3. fraction numerator 1 over denominator square root of 3 end fraction    
  4. square root of fraction numerator 2 over denominator 3 end fraction end root    

The correct answer is: fraction numerator 1 over denominator square root of 6 end fraction


    B D colon D C equals 1 colon 3
    T o blank c a l c u l a t e blank colon fraction numerator s i n invisible function application angle B A D over denominator s i n invisible function application divided by C A D end fraction

    Hint: Apply sine rule in ∆ABD,
    fraction numerator A D over denominator sin invisible function application fraction numerator pi over denominator 3 end fraction end fraction equals fraction numerator B D over denominator s i n invisible function application angle B A D end fraction
    In ∆CAD,
    fraction numerator A D over denominator sin invisible function application fraction numerator pi over denominator 4 end fraction end fraction equals fraction numerator D C over denominator s i n invisible function application angle C A D end fraction
    From Eqs. (1) and (2), we get
    fraction numerator square root of 3 over denominator 2 end fraction times fraction numerator B D over denominator s i n angle B A D end fraction equals fraction numerator 1 over denominator square root of 2 end fraction times fraction numerator D C over denominator s i n angle C A D end fraction
    table row cell rightwards double arrow fraction numerator square root of 3 over denominator 2 end fraction times open parentheses fraction numerator B D over denominator D C end fraction close parentheses cross times square root of 2 equals fraction numerator s i n invisible function application angle B A D over denominator s i n invisible function application angle C A D end fraction end cell row cell rightwards double arrow fraction numerator square root of 3 over denominator 2 end fraction cross times fraction numerator 1 over denominator 3 end fraction cross times square root of 2 equals fraction numerator s i n invisible function application angle B A D over denominator s i n invisible function application angle C A D end fraction end cell row cell rightwards double arrow fraction numerator s i n invisible function application angle B A D over denominator s i n invisible function application angle C A D end fraction equals fraction numerator 1 over denominator square root of 6 end fraction end cell end table

    Related Questions to study

    General
    Chemistry-

    The compound with the highest boiling point is:

    The compound with the highest boiling point is:

    Chemistry-General
    General
    Chemistry-

    Give the decreasing order of reactivity of Diels-Alder reactions for the following:
    I)
    II)
    III)
    IV)

    Give the decreasing order of reactivity of Diels-Alder reactions for the following:
    I)
    II)
    III)
    IV)

    Chemistry-General
    General
    Chemistry-

    The decreasing order of boiling points of the following compounds is:
    I)
    II)
    III)
    IV) 

    The decreasing order of boiling points of the following compounds is:
    I)
    II)
    III)
    IV) 

    Chemistry-General
    parallel
    General
    Chemistry-

     Compounds (B) and (C) are:

     Compounds (B) and (C) are:

    Chemistry-General
    General
    Chemistry-

    Which reagents could be used to carry out the following reaction?

    Which reagents could be used to carry out the following reaction?

    Chemistry-General
    General
    Chemistry-

    Hydrogenation of the adjoining compound in the presence of poisoned palladium catalyst gives:

    Hydrogenation of the adjoining compound in the presence of poisoned palladium catalyst gives:

    Chemistry-General
    parallel
    General
    Chemistry-

    Arrange the following in the decreasing order of their boiling points
    I)
    II)
    III)
    IV) 

    Arrange the following in the decreasing order of their boiling points
    I)
    II)
    III)
    IV) 

    Chemistry-General
    General
    Chemistry-

     The product is:

     The product is:

    Chemistry-General
    General
    Chemistry-

    Chemistry-General
    parallel
    General
    Chemistry-

    Which of the following products would produce a racemic mixture on monochlorination?
    I)
    II)
    III)
    IV) 

    Which of the following products would produce a racemic mixture on monochlorination?
    I)
    II)
    III)
    IV) 

    Chemistry-General
    General
    Chemistry-

     (B) and (C ) are:

     (B) and (C ) are:

    Chemistry-General
    General
    Chemistry-

     Which reagent is used for the conversion of (A) to (B) ?

     Which reagent is used for the conversion of (A) to (B) ?

    Chemistry-General
    parallel
    General
    Maths-

    The Area of the region between x-y+2=0 and the curve x =blank square root of y blankis…

    The Area of the region between x-y+2=0 and the curve x =blank square root of y blankis…

    Maths-General
    General
    Maths-

    T h e blank a r e a blank l y i n g blank i n blank t h e blank f i r s t blank q u a d r a n t blank b e t w e e n blank t h e blank c u r v e s blank x to the power of 2 end exponent plus y to the power of 2 end exponent equals pi to the power of 2 end exponent blank a n d blank y equals s i n blank x blank a n d blank y minus a x i s blank i s

    T h e blank a r e a blank l y i n g blank i n blank t h e blank f i r s t blank q u a d r a n t blank b e t w e e n blank t h e blank c u r v e s blank x to the power of 2 end exponent plus y to the power of 2 end exponent equals pi to the power of 2 end exponent blank a n d blank y equals s i n blank x blank a n d blank y minus a x i s blank i s

    Maths-General
    General
    Maths-

    T h e blank a r e a blank c o m m o n blank t o blank t h e blank c i r c l e blank x to the power of 2 end exponent plus y to the power of 2 end exponent equals 16 a to the power of 2 end exponent blank a n d blank y to the power of 2 end exponent equals 6 a x blank i s

    T h e blank a r e a blank c o m m o n blank t o blank t h e blank c i r c l e blank x to the power of 2 end exponent plus y to the power of 2 end exponent equals 16 a to the power of 2 end exponent blank a n d blank y to the power of 2 end exponent equals 6 a x blank i s

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.