MathematicsIn a right-angled triangle if tanθ= 3 4 ,   then what would be the measure of the greatest side of the triangle?

In a right-angled triangle if tanθ= 3 4 ,   then what would be the measure of the greatest side of the triangle?


  1. A
    5 units
  2. B
    6 units
  3. C
    7 units
  4. D
    9 units 

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    Solution:

    The given trigonometric ratio is,
    tanθ= 3 4  .
    We know that,
    tanθ=  Perpendicular   Base    Therefore, we have,
    Perpendicular =3.
    Base = 4.
    Using the Pythagoras theorem, we have,  Hypotenus e 2 = Perpendicula r 2 + Bas e 2   Hypotenuse= 3 2 + 4 2 Hypotenuse = 25 Hypotenuse=5  
    In a right-angled triangle, the greatest side is the hypotenuse of the triangle.
    Therefore, the measure of the greatest side of the triangle is 5 units.
    Hence, option (1) is correct.
     
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