The mistake that the student did here was that he applied tangent ratio to a triangle which is not sure being a right angled triangle.
On which triangle can we apply trigonometric ratios?
Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).
Here, we don't know if the angle between the side of length 6.5 and of length 2.5 is 90 degrees (which is needed for those sides to be called as perpendicular and base from the perspective of angle α.
Thus, the mistake that the student did here was that he applied tangent ratio to a triangle which is not sure being a right angled triangle.
Learn more about trigonometric ratios here:
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