Final answer:
By using the sum of angles in a triangle and the Law of Sines, we found the length of side a in △ABC to be approximately 46 when rounded to the nearest whole number, making option b) 46 the correct answer.
Step-by-step explanation:
To answer the question about the length of side a in △ABC given that c = 72, m∠C = 41°, and m∠A = 23°, we first need to find m∠B using the fact that the sum of angles in a triangle is 180°. Subtracting the given angles from 180°, we get m∠B = 180° - 41° - 23° = 116°.
Next, to find the length of side a, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for any side/angle pair in the triangle. Thus, we have: a/sinA = c/sinC
Plugging in the known values:
a/sin23° = 72/sin41°
Solving for a gives us the length we are looking for. Upon calculating, we find that a ≈ 46 is rounded to the nearest whole number. Therefore, the correct option is b) 46.