Question
Find u in this 30-60-90 triangle.
- u = 6
Hint:
We are given a right-angled triangle. We are given one of its side. It is 30°. The other angle will be 60°. We are given the values of its hypotenuse. We are asked to find the value of its one of the side. It is denoted by “u".
The correct answer is: u = 6
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 30°
∠BCA = 60°
BC = v
AC = 4√3
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.
Length of smallest side = v
Hypotenuse = 4√3
So we can write,
Hypotenuse = 2(length of the smallest side)
4√3 = 2v
So, to find the smaller leg we have to divide the hypotenuse by 2.
v = 4√3 ÷ 2
v = 2√3
Now,
Length of longer side = √3(length of smaller side)
u = √3(v)
u = √3 × 2√3
u = 6
Therefore, the length of u is 6.
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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