Question
Find x.
- 10
- 20
Hint:
We are given a right-angled triangle. We are given one of its side. It is a 30°-60°-90° triangle. We are asked to find the value of its other side. It is denoted by the variable “x”.
The correct answer is:
Let the given triangle be ABC.
∠ABC = 90°
∠BCA = 60°
∠BAC = 30°
BC = 10.
AB = x
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. The side opposite to 60° is AB.
Length of smallest side= 10
Length of longest side = x
So we can write,
Length of longer side = √3(length of smaller side)
AB = √3(BC)
x = √3(10)
x = 10√3
Therefore, the length of x is 10√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 using trigonometric ratios.
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