Question
Find x.
- 4
- 2
Hint:
We are given a right-angled triangle. We are given one of its angle. It is 60°. Then, the other angle will be 30°. We are given the values of its two sides. We are asked to find the values of the hypotenuse. It is denoted by the variable “x”.
The correct answer is: 4
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 60°
AB = 2
BC = 2√3
The sum of all angles of a triangle is 180°. Therefore, the remaining angle will be 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.
In the given question, the smallest side is 2.
The longer side is 2√3.
So we can write,
Length of hypotenuse = 2 (length of smallest side)
x = 2(2)
x = 4
Therefore, the length of the hypotenuse is 4.
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.
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