Final answer:
After attempting to solve for the angles of the triangle, we find that the sum of the converted angles exceeds 180 degrees, indicating a mistake in the given ratios. It is not possible for the angles provided in the question to form a valid triangle, as their sum must always equal 180 degrees on a plane.
Step-by-step explanation:
To solve the problem, we need to convert the given ratios into a common unit, which is usually degrees, since a triangle has three angles that add up to 180 degrees. The ratios have been given in degrees, grades, and radians (72:70:4π), respectively. Given that 1 radian is equal to 57.3 degrees, and there are 400 grades in a full circle, which is also 360 degrees, we can convert 70 grades into degrees using the ratio (360 degrees/400 grades), and we can convert 4π radians into degrees by multiplying 4π by 57.3 degrees/radian.
First, we convert the second angle from grades to degrees: 70 grades * (360 degrees / 400 grades) = 63 degrees.
Next, we convert the third angle from radians to degrees: 4π radians * (57.3 degrees / radian) = 4π * 57.3 degrees ≈ 4 * 3.1416 * 57.3 degrees ≈ 720 degrees.
Now that we have all three angles in degrees, we can set up the equation:
72 degrees + 63 degrees + 720 degrees = 855 degrees
The sum of the angles in this hypothetical triangle exceeds 180 degrees, which is not possible for any triangle. There seems to be a misunderstanding or typo in the given ratios, since any triangle's angles in a plane must always add up to 180 degrees. There is no way for the angles provided in the question to form a valid triangle, so the question cannot be solved accurately with the given information.