Question
Determine the value of y.
- 6
- 1
Hint:
We are given a right-angled triangle. We are given two of its angle. It is 30°-60°-90° triangle. We are given the values of one of its side. It is 6. We are asked to find it’s hypotenuse.
The correct answer is:
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 30°
AB = 6
BC = x
AC = y
The sum of all angles of a triangle is 180°. Therefore, the remaining angle will be 30°
So, ∠BCA = 30°
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 smallest side = x
Hypotenuse = y
Length of longer side = 6
So we can write,
Length of longer leg = √3 ( length of smaller leg)
AB = √3(BC)
So, to find the smaller leg we have to divide the longer side by √3.
BC = AB ÷ √3
BC = 6 ÷ √3
BC = 2√3
Now,
Hypotenuse = 2(length of smallest side)
AC = 2(2√3)
y = 4√3
Therefore, the length of the hypotenuse is 4√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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