Question
Find b in this 30-60-90 triangle.
- b = 7.5
- b = 7
Hint:
We are given a right-angled triangle. We are given one of its side. It is a 30°-60°-90° triangle. We are asked to find the value of its other side. It is denoted by the variable “b”.
The correct answer is: b = 7
Let the given triangle be ABC.
∠ABC = 90°
∠BAC = 60°
BC = 7√3
AB = b
The sum of angles of a triangle is 180°.
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. The side opposite to 60° is BC.
Length of smallest side= b
Length of longest side = 7√3
So we can write,
Length of longer side = √3(length of smaller side)
BC = √3(AB)
7√3 = √3(b)
We will divide the both sides by √3 and rearranging the equation for b. b = 7√3 ÷ √3
b = 7
Therefore, the length of b is 7.
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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