To find the largest angle of triangle APM, we can use the law of cosines which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the side opposite the angle we want to find, a and b are the other two sides, and C is the angle opposite side c.
In this case, we want to find angle APM, which is opposite side m, so we can use:
m^2 = p^2 + a^2 - 2pa*cos(APM)
Solving for cos(APM), we get:
cos(APM) = (p^2 + a^2 - m^2) / (2pa)
Plugging in the given values, we get:
cos(APM) = (16^2 + 9^2 - 22^2) / (2169) = -0.239
Since cosine is negative, angle APM must be obtuse. To find the size of the angle, we can use the inverse cosine function:
APM = cos^-1(-0.239) = 103.46 degrees
Therefore, the largest angle of triangle APM is approximately 103.46 degrees.