Final answer:
The angle of elevation of the sun is determined using the right-angled triangle formed by the pole and its shadow. As both the pole's height and the shadow's length are 50 feet, it is a 45-45-90 triangle, making the sun's angle of elevation 45 degrees.
Step-by-step explanation:
The student is attempting to find the angle of elevation of the sun, given a pole that casts a shadow equal in length to its height. This situation forms a right-angled triangle, with the pole as the vertical side, the shadow as the horizontal side, and the line of sight from the top of the pole to the tip of the shadow as the hypotenuse. Since the lengths of the pole and the shadow are equal, this triangle is a 45-45-90 triangle, meaning the angles opposite the equal sides are 45 degrees each.
To find the angle of elevation of the sun, we can use the fact that at the point where the shadow is being cast, the angle between the horizontal ground and the line of sight to the sun is the same as the angle between the ground and the line from the bottom of the pole to the tip of the shadow. This is because the rays of the sun are coming down at this angle, making the shadow. Thus, the angle of elevation of the sun is 45 degrees.