Final answer:
To sketch a triangle with an acute angle θ and given cosine value, use the inverse cosine function to find the remaining side length.
Step-by-step explanation:
To sketch a triangle with an acute angle θ and given cosine value, we can use the inverse cosine function. Since cosine is the ratio of the adjacent side to the hypotenuse, we can create a triangle with a side length of 9 and a hypotenuse of 40. To find the remaining side, we can use the Pythagorean theorem. Let's denote the remaining side as x. Using the equation x^2 = 40^2 - 9^2, we can solve for x to find the length of the remaining side. With all three sides known, we can draw a triangle with an acute angle θ.