We can start by using the Law of Cosines to determine if the triangle is acute or obtuse. The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c:
c^2 = a^2 + b^2 - 2ab cos(C)
Using this formula, we can determine that:
7^2 = 5^2 + 6^2 - 2(5)(6)cos(75°)
49 = 25 + 36 - 60cos(75°)
cos(75°) = (25 + 36 - 49) / (2(5)(6))
cos(75°) = -0.087
Since the cosine of 75° is negative, the angle C opposite side c = 7 cm is greater than 90°, and the triangle is obtuse.
Next, we can look at the angles of the triangle. The angle opposite the side of length 5 cm is 60°, which means that the other two angles must add up to 120°. Since the triangle is obtuse, one of these angles must be greater than 90°, which means that the triangle cannot be isosceles. Therefore, the triangle is an obtuse scalene triangle.
The correct answer is C) obtuse scalene triangle.