Final answer:
To find the value of 'a' such that sin a = cos 20°, we use the complementarity of sine and cosine. The complement of 20° is 70°, hence the correct answer is B. 70°.
Step-by-step explanation:
To determine what value of a makes the statement sin a = cos 20° true, we can use the fact that the sine of an angle is equal to the cosine of its complement. The complement of an angle is what you would subtract from 90° to get that angle. Therefore, if sin a = cos 20°, then a must be the complement of 20°, which would be 90° - 20° = 70°.
Answer: B. 70° is the value of a that makes the statement true.