In this case, the dimensions of 12 inches in width and 4 inches in length are not crucial for solving the problem. An equation has been provided already, and it clearly states that A, as a function of θ, represents the area of the opening. We are specifically instructed to find this area, and the value of θ has been given. Therefore, the initial details seem to serve merely as a distraction.
Hence, we can directly substitute θ=45° into the given function.
A = 16 sin 45° ⋅ (cos 45° + 1)
Since 45° is a notable angle in trigonometry, remembering its functions is straightforward. The sine of 45° is √2/2, and the cosine of 45° is also √2/2.
A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8 + 8√2
A = 19.31 square inches
