The correct equations for solving for x in a right triangle with an angle of 28 degrees and hypotenuse of 5 are x = 5 cos(28) or cos(28) = x/5. Options c and e are incorrect due to misalignment of trigonometric ratios, and option e includes an incorrect tangent ratio.
The correct equations that could be used to solve for x are:
a) x = 5 cos(28): This equation uses the cosine ratio of the angle 28 degrees and the hypotenuse 5 to find the adjacent side x.
b) cos(28) = x/5: This equation is equivalent to the previous one, but rearranged by dividing both sides by 5.
d) x = 5 sin(28): This equation uses the sine ratio of the angle 28 degrees and the hypotenuse 5 to find the opposite side x.
The other two options are incorrect because:
c) sin(28) = x/5: This equation is not equivalent to option d, but rather to the inverse of option d, which is x = 5/sin(28).
e) x = 5 tan(28): This equation uses the tangent ratio of the angle 28 degrees and the hypotenuse 5 to find the opposite side x, but this is not the correct ratio for a right triangle. The correct ratio is x = 5 tan(28)/sqrt(1 + tan^2(28)).