Mathematics
Grade9
Easy

Question

Find y.

  1. 3
  2. 9
  3. 6square root of 3
  4. 6 square root of 2

hintHint:

We are given a right-angled triangle. We are given one of its angle. It is a 30°-60°-90° triangle. We are given the value of its hypotenuse. It is 12. We are asked to find the value of the other side. It is denoted by “y”.

The correct answer is: 6square root of 3


    Let the given triangle be ABC.
    ∠ABC = 90°
    ∠BAC = 30°
    ∠ACB = 30°
    AB = y
    BC = x
    AC = 12
    It is 30°-60°-90° triangle.
    In a 30°-60°-90° triangle, the length of hypotenuse is two times the length of the smallest side. It’s longer side is √3 times the value of the smallest side.
    The side opposite to the 30° angle is the smallest side.
    The side opposite to the 60° angle is the longer side.
    In the given question, the side opposite to 30° is BC. And the side opposite to 60° is AB.
    Length of the smaller side = x
    Length of the longer side = y
    Hypotenuse = 12
    So we can write,
    Hypotenuse = 2(length of smallest side)
    AC = 2(BC)
    12 = 2(x)
    We will divide both the sides by 2 and rearrange the equation for “a”.
    x = 12 ÷ 2
    x = 6
    Therefore, the value of x is 6.
    Length of longer side = √3(length of the smallest side)
    AB = √3(BC)
    y = √3(6)
    The length of y is 6√3.

    For such questions, we should know about the properties of a right-angled triangle and 30°-60°-90° triangle. The alternate way to solve the above question is by Pythagoras theorem and trigonometric ratios.

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