Question
Find the value of x.
- 1
- 4
- 2
Hint:
We are given a right-angled triangle. It is a 30°-60°-90° triangle. We are given the value of its hypotenuse. We are asked to find the value of one of the sides. It is denoted by “x”. We will use the properties of 30°-60°-90° triangle.
The correct answer is: 4
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 30°
∠BCA = 60°
BC = y
AB = x
AC = 8
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 AB.
The side opposite to the 60° is BC.
Length of smallest side = x
Hypotenuse = 8
So we can write,
Hypotenuse = 2(length of the smallest side)
8 = 2x
So, to find the smaller leg we have to divide the hypotenuse by 2.
x = 8 ÷ 2
x = 4
Therefore, the value of x 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 and trigonometric ratios.
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