Final answer:
The value of c is best represented by the expression tan45° multiplied by b, which simplifies to just b because tan45° is equal to 1.
Step-by-step explanation:
The expression that represents c when given c is the value of tan45°b would simply be tan45° multiplied by b. In trigonometry, tan45° is equal to 1 because the tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side, and at 45 degrees, these two sides are equal, making the ratio 1. Thus, multiplying 1 by any value b will give us the value of b itself.
The options cos45°b and acos45° is incorrect because cosine is a different trigonometric function, and atan45° suggests taking the arctangent or inverse of tan45°, which is unnecessary since we already have a direct tangent value. Therefore, A) tan45°b is the most accurate representation of c.