Question

If the angles of a triangle are in the ratio 1:2:3 then the smallest angle in radian is​

Answer 1

Answer:

π/6

Step-by-step explanation:

According to your question, angles are in the ratio 1 : 2 : 3.

Let us consider the angle of the triangle are x , 2x and 3x respectively.

As sum of all angles in the triangle is 180 degree.

∴  x + 2x + 3x = 180

∴ 6x = 180

∴ x = 30

Angles are 30 , 60 and 90 degree.

So , the smallest angle of all is 30 degree.

∴ smallest angle in radian is π/6.

Answer 2

Given: If the angles of a triangle are in the ratio 1:2:3

To find: The smallest angle in radian.

Solution:

Let the first angle of the triangle be x. Then, the other two angles could be written as 2x and 3x. Since the sum of all the angles of a triangle must sum up to give a total of 180°, the following equation can be formed.

$x+2x+3x=180$

$6x=180$

$x=30$

$2x = 60$

$3x = 90$

Thus, the three angles of the triangle are 30°, 60° and 90°. The smallest of them is 30°. Now, an angle can be converted from degrees to radians by multiplying it with π/180. Thus, 30° can be written in radian as follows.

$30 * \frac{\pi }{180} = \frac{\pi }{60}$

Therefore, the smallest angle in radian is π/6.