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Question
Select the correct option from the given alternatives :
If the angles of a triangle are in the ratio 1 : 2 : 3, then the smallest angle in radian is ______.
Options
`pi/3`
`pi/6`
`pi/2`
`pi/9`
Solution
If the angles of a triangle are in the ratio 1 : 2 : 3, then the smallest angle in radian is `pi/6`.
Explanation:
The sum of the angles in a triangle is always `180^circ` or π radians.
If the angles are in the ratio 1 : 2 : 3 let the angles be x, 2x, and 3x, where x is the common factor.
The sum of the angles is:
x + 2x + 3x = π
6x = π
x = `pi/6`
∴ The smallest angle corresponds to the smallest ratio, which is x.
Thus, the smallest angle is `pi/6`radians.
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