Question
The side is the short leg of this 30-60-90 triangle is?
- 6
- m
- n
- a
Hint:
We are given a right-angled triangle. It is a 30°-60°-90°. The length of hypotenuse is 6. The length of other two sides is given using variables. We are asked to find the leg which is shorter.
The correct answer is: n
Let the given triangle be ABC.
∠ABC = 90°
∠ACB = 60°
AB = m
BC = n
AC = 6
∠CAB = 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.
From the figure, the side opposite to 30° is BC.
The value of BC = n.
So, the side “n” is the shorter leg.
For such questions, we should know about different properties of different triangles.
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