Question
The long leg of a 30 - 60 - 90 is 18√3 units. Find the length of the hypotenuse.
- 36 units
- 18 units
- 18
units - 18
units
units units
Hint:
We are given a right-angled triangle. It is 30°-60°-90° triangle. We are given the length of its long leg. It is 18√3 units. We are asked to find it’s hypotenuse.
The correct answer is: 36 units
Let the given triangle be ABC.
∠ABC = 90°
∠CAB = 60°
∠BCA = 30°
BC = 18√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 AB. And the side opposite to 60° is BC.
Length of long leg = 18√3 units
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 = 18√3 ÷ √3
AB = 18 units.
Now,
Hypotenuse = 2(length of small leg)
AC = 2(18)
AC = 36 units.
Therefore, the length of the hypotenuse is 36 units.
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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