Question
______ long is e.
- 3
- 6
Hint:
We are given a right-angled triangle. We are given one of its angle. It is 60°. The other angle will be 30°. We are given the values of one of its side. It is 3√3. We are asked to find it’s hypotenuse.
The correct answer is: 6
Let the given triangle be ABC.
∠ABC = 90°
∠CAB = 60°
∠BCA = 30°
AB = c
BC = 3√3
AC = e
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 AB. And the side opposite to 60° is BC.
Length of smallest side = c
Hypotenuse = e
Length of longer side = 3√3
So we can write,
Length of longer leg = √3 ( length of smaller leg)
BC = √3(AB)
So, to find the smaller leg we have to divide the longer side by √3.
AB = BC ÷ √3
AB = 3√3 ÷ √3
AB = 3
Now,
Hypotenuse = 2(length of smallest side)
AC = 2(3)
e = 6
Therefore, the length of the hypotenuse 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 trigonometric ratios.
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