MathematicsIn the figure given below, ΔABC   is right angled at B such that BC=3 cm and AB=4 cm,  then which of the following is the value of sinA and cosA  ?

In the figure given below, ΔABC   is right angled at B such that BC=3 cm and AB=4 cm,  then which of the following is the value of sinA and cosA  ?


In the given figure ABC is a right triangle and right angled at B such that  BCA = 2 BAC .Show that hypotenuse AC = 2BC.(Hint : Produce CB to a point

  1. A
    sinA= 4 5  & cosA= 3 5  
  2. B
    sinA= 3 5  & cosA= 4 5  
  3. C
    sinA= 5 4  & cosA= 5 3  
  4. D
    sinA= 5 3  & cosA= 5 4   

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    Solution:

    Given that ΔABC   is right angled at B such that BC=3 cm and AB=4 cm.  
    In the given figure ABC is a right triangle and right angled at B such that  BCA = 2 BAC .Show that hypotenuse AC = 2BC.(Hint : Produce CB to a pointTherefore, by using Pythagoras theorem in ΔABC  , we have,
    Hypotenuse 2 = Perpendicular 2 + Base 2  
    A C 2 =B C 2 +B A 2 A C 2 = 3 2 + 4 2 A C 2 =25 AC=5 cm  
    From the figure,
    sinA= BC AC sinA= 3 5  
    and cosA= AB AC cosA= 4 5  
    Therefore, the values of sinA= 3 5  & cosA= 4 5 .  
    Hence, option (2) is correct.
     
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