Question
I have been given the long leg in this 30-60-90 triangle. Choose the correct way to find the short leg.
- Multiply 7 by 2
- Multiply 7 by
- Divide 7 by 2
- Divide 7 by
Hint:
We are given a right-angled triangle. We are given one of its angle. It is 30°. Then, the other angle will be 60°. We are given the values of its long leg. It is 7. We are asked to find the value of the short leg.
The correct answer is: Divide 7 by
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 30°
AB = y
BC = 7
AC = x
The sum of all angles of a triangle is 180°. Therefore, the remaining angle will be 30°
So, ∠BCA = 60°
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.
Length of smallest side = y
Hypotenuse = x
The length of longer side is 7.
So we can write,
Length of longer leg = √3 ( length of smaller leg)
So, to find the smaller leg we have to divide the longer side by √3.
To solve such questions, we should know the properties of different triangles.
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