We notice from the choices, that the problem is solved using the Pythagorean theorem somehow. How?
If ABC was a right triangle, the hypotenuse would be BC (the largest side), so the right angle would be A.
In that case we would have 54 squared (which equals 2916) equal to the sum of the squares of 22 and 51 (which equals 3085).
If the triangle was a right triangle, [tex]22^2+51^2[/tex] would be exactly equal to [tex]54^2[/tex], but it is larger. This means that a right angle is not large enough to 'enclose' [tex]22^2+51^2[/tex]. Thus angle A must be opened more that 90°.
Thus the answer is D:
an obtuse triangle because [tex]22^2+51^2>54^2[/tex]
