Question
Find y.
- 3
- 9
- 6
Hint:
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: 6
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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