Final answer:
The angle θ that the ladder makes with the ground is approximately 37°, based on the given information and the use of the cosine trigonometric function.
Step-by-step explanation:
The student has a math problem involving a ladder resting against a wall. Using trigonometry, we find the angle θ that the ladder makes with the ground. Given that the ladder is 5 meters long and reaches a vertical height of 3 meters on the wall, we can use the Pythagorean theorem to find the horizontal distance from the base of the wall to the ladder, which is 4 meters. Hence, we have a right triangle with sides of 3 meters (opposite), 4 meters (adjacent), and 5 meters (hypotenuse).
To find the angle θ, we can use the trigonometric function cosine, such that cos(θ) = adjacent/hypotenuse = 4/5. Using a calculator, cos-1(0.8) gives us the angle θ, which is approximately 36.87°. The closest angle choice from the options given in the question is 37°, which is the approximate measure of the angle that the ladder makes with the ground.