Maths-
General
Easy

Question

In a triangle ABC, if a : b : c = 7 : 8 : 9, then cos A : cos B equals to

  1. 11 over 63    
  2. 22 over 63    
  3. 2 over 9    
  4. 14 over 11    

hintHint:

Use cosine formula to obtain the ratio of cosA and cosB.

The correct answer is: 14 over 11


    U sin g space cos i n e space f o r m u l a comma
cos A equals fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction
cos B equals fraction numerator a squared plus c squared minus b squared over denominator 2 a c end fraction

G i v e n comma
a colon b colon c equals 7 colon 8 colon 9
a equals 7 k comma b equals 8 k comma c equals 9 k

cos A equals fraction numerator open parentheses 8 k close parentheses squared plus open parentheses 9 k close parentheses squared minus open parentheses 7 k close parentheses squared over denominator 2 open parentheses 8 k close parentheses open parentheses 9 k close parentheses end fraction equals fraction numerator 64 k squared plus 81 k squared minus 49 k squared over denominator 2 open parentheses 8 k close parentheses open parentheses 9 k close parentheses end fraction equals fraction numerator 96 k squared over denominator 2 open parentheses 8 k close parentheses open parentheses 9 k close parentheses end fraction equals 2 over 3
cos B equals fraction numerator open parentheses 7 k close parentheses squared plus open parentheses 9 k close parentheses squared minus open parentheses 8 k close parentheses squared over denominator 2 open parentheses 7 k close parentheses open parentheses 9 k close parentheses end fraction equals fraction numerator 49 k squared plus 81 k squared minus 64 k squared over denominator 2 open parentheses 7 k close parentheses open parentheses 9 k close parentheses end fraction equals fraction numerator 66 k squared over denominator 2 open parentheses 7 k close parentheses open parentheses 9 k close parentheses end fraction equals 11 over 21

S o comma
cos A colon cos B equals 2 over 3 colon 11 over 21 equals 14 colon 11

    Related Questions to study

    General
    physics-

    Which of the following curves represents correctly the oscillation given by y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90

    Which of the following curves represents correctly the oscillation given by y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90

    physics-General
    General
    maths-

    A is a set containing n elements. A subset P1 is chosen, and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1 union P2 union … union Pm= A is -

    A is a set containing n elements. A subset P1 is chosen, and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1 union P2 union … union Pm= A is -

    maths-General
    General
    maths-

    The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x| less or equal than k, |y| less or equal than k, |x – y| less or equal than k ; is-

    The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x| less or equal than k, |y| less or equal than k, |x – y| less or equal than k ; is-

    maths-General
    parallel
    General
    Maths-

    The angle between the lines r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3 and r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0 is

    Here we used the concept of cartesian lines and some trigonometric terms to solve. With the help of slope we identified the angle between them. Hence, these lines are perpendicular so the angle between them is 90 degrees.

    The angle between the lines r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3 and r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0 is

    Maths-General

    Here we used the concept of cartesian lines and some trigonometric terms to solve. With the help of slope we identified the angle between them. Hence, these lines are perpendicular so the angle between them is 90 degrees.

    General
    maths-

    The polar equation of the straight line passing through open parentheses 6 comma fraction numerator pi over denominator 3 end fraction close parentheses and perpendicular to the initial line is

    The polar equation of the straight line passing through open parentheses 6 comma fraction numerator pi over denominator 3 end fraction close parentheses and perpendicular to the initial line is

    maths-General
    General
    maths-

    The polar equation of the straight line passing through open parentheses 2 comma fraction numerator pi over denominator 6 end fraction close parentheses and parallel to the initial line is

    The polar equation of the straight line passing through open parentheses 2 comma fraction numerator pi over denominator 6 end fraction close parentheses and parallel to the initial line is

    maths-General
    parallel
    General
    Maths-

    The equation of the line passing through pole and open parentheses 2 comma fraction numerator pi over denominator 3 end fraction close parentheses is

    The equation of the line passing through pole and open parentheses 2 comma fraction numerator pi over denominator 3 end fraction close parentheses is

    Maths-General
    General
    Maths-

    The polar equation of y to the power of 2 end exponent equals 4 x is

    Here we used the concept of polar coordinate system and also the trigonometric ratios to find the solution. So the equation is r equals 4 space c o t space theta space cos e c space theta.

    The polar equation of y to the power of 2 end exponent equals 4 x is

    Maths-General

    Here we used the concept of polar coordinate system and also the trigonometric ratios to find the solution. So the equation is r equals 4 space c o t space theta space cos e c space theta.

    General
    Maths-

    The cartesian equation of r equals a s i n space 2 theta is

    Here we used the concept of the polar coordinate system and also the trigonometric ratios to find the solution. So the equation is 4 a squared x squared y squared equals left parenthesis x squared plus y squared right parenthesis cubed.

    The cartesian equation of r equals a s i n space 2 theta is

    Maths-General

    Here we used the concept of the polar coordinate system and also the trigonometric ratios to find the solution. So the equation is 4 a squared x squared y squared equals left parenthesis x squared plus y squared right parenthesis cubed.

    parallel
    General
    physics-

    Two tuning forks P and Q are vibrated together. The number of beats produced are represented by the straight line O A in the following graph. After loading Q with wax again these are vibrated together and the beats produced are represented by the line O B. If the frequency of P is 341 H z comma the frequency of Q will be

    Two tuning forks P and Q are vibrated together. The number of beats produced are represented by the straight line O A in the following graph. After loading Q with wax again these are vibrated together and the beats produced are represented by the line O B. If the frequency of P is 341 H z comma the frequency of Q will be

    physics-General
    General
    Maths-

    If a hyperbola passing through the origin has 3 x minus 4 y minus 1 equals 0 and 4 x minus 3 y minus 6 equals 0 as its asymptotes, then the equation of its tranvsverse and conjugate axes are

    Here we used the concept of polar coordinate system and also the trigonometric ratios to find the solution. T h e space e q u a t i o n space o f space t r a n s v e r s e space i s space x plus y minus 5 equals 0. space T h e space e q u a t i o n space o f space c o n j u g a t e space a x i s space i s space x minus y minus 1 equals 0.

    If a hyperbola passing through the origin has 3 x minus 4 y minus 1 equals 0 and 4 x minus 3 y minus 6 equals 0 as its asymptotes, then the equation of its tranvsverse and conjugate axes are

    Maths-General

    Here we used the concept of polar coordinate system and also the trigonometric ratios to find the solution. T h e space e q u a t i o n space o f space t r a n s v e r s e space i s space x plus y minus 5 equals 0. space T h e space e q u a t i o n space o f space c o n j u g a t e space a x i s space i s space x minus y minus 1 equals 0.

    General
    maths-

    Five distinct letters are to be transmitted through a communication channel. A total number of 15 blanks is to be inserted between the two letters with at least three between every two. The number of ways in which this can be done is -

    Five distinct letters are to be transmitted through a communication channel. A total number of 15 blanks is to be inserted between the two letters with at least three between every two. The number of ways in which this can be done is -

    maths-General
    parallel
    General
    maths-

    The number of ordered pairs (m, n), m, n element of {1, 2, … 100} such that 7m + 7n is divisible by 5 is -

    The number of ordered pairs (m, n), m, n element of {1, 2, … 100} such that 7m + 7n is divisible by 5 is -

    maths-General
    General
    maths-

    Consider the following statements:
    1. The number of ways of arranging m different things taken all at a time in which p less or equal than m particular things are never together is m! – (m – p + 1)! p!.
    2. A pack of 52 cards can be divided equally among four players in order in fraction numerator 52 factorial over denominator left parenthesis 13 factorial right parenthesis to the power of 4 end exponent end fractionways.
    Which of these is/are correct?

    Consider the following statements:
    1. The number of ways of arranging m different things taken all at a time in which p less or equal than m particular things are never together is m! – (m – p + 1)! p!.
    2. A pack of 52 cards can be divided equally among four players in order in fraction numerator 52 factorial over denominator left parenthesis 13 factorial right parenthesis to the power of 4 end exponent end fractionways.
    Which of these is/are correct?

    maths-General
    General
    maths-

    The total number of function ‘ƒ’ from the set {1, 2, 3} into the set {1, 2, 3, 4, 5} such that ƒ(i) less or equal than ƒ(j), straight for all i < j, is equal to-

    The total number of function ‘ƒ’ from the set {1, 2, 3} into the set {1, 2, 3, 4, 5} such that ƒ(i) less or equal than ƒ(j), straight for all i < j, is equal to-

    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.