Final answer:
The area of triangle △ABC could be found using the formula 1/2 × b × c × sin(∠A). Angle B can be found using the sum of triangle angles. However, the value of side c is required to find the area, and it was not provided.
Step-by-step explanation:
To find the area of a triangle with two angles and one side known (△ABC with ∠A = 23°, ∠C = 39°, and b = 14.6), we can use the formula for the area of a triangle when given two angles and a side between them, which is Area = 1/2 × b × c × sin(∠A).
First, calculate the third angle ∠B using the fact that the sum of all angles in a triangle is 180°. ∠B = 180° - ∠A - ∠C = 180° - 23° - 39° = 118°.
Now, we need side c, which can be found using the Law of Sines: c/sin(∠C) = b/sin(∠B). After calculating c, we can find the area.
However, without the value of side c, we cannot solve this problem directly. The provided information is insufficient or the question appears incomplete as it stands.