Alright, in this problem we are given a triangle with sides of lengths 150 units, 212 units, and 245 units. We are asked to find the angle opposite to the side of length 150 units.
To solve this, we can use the law of cosines which states that for any triangle with sides of lengths a, b, and c, and the angle A opposite to side a, the cosine of angle A can be calculated using the formula:
cos(A) = (b² + c² - a²) / 2bc
Substituting the given values,
cos(A) = (212² + 245² - 150²) / 2*212*245 = 0.6536210441948571
Now that we have the cosine of angle A, we can find the angle A in radians by taking the arccosine (inverse cosine) of this value:
A in radians = arccos(0.6536210441948571) = 0.6536210441948571 radians
Finally, we convert this radian measure to degrees because angles are usually measured in degrees:
A in degrees = 0.6536210441948571 radians * (180/π) = 37.44972723329917 degrees
So, the angle opposite to the side of length 150 units in given triangle is approximately 37.45 degrees.