two fences, 16 ft apart, are to be constructed so that the first fence is 2 ft high and the second fence is higher then the first. what is the length of the shortest pole that has one end on the ground, passes over the first fence, and then reaches the second fence?
To find the length of the shortest pole, we need to consider the given information. We have two fences with a 16 ft distance between them, and the first fence is 2 ft high. Let's break down the problem into steps and find a solution:
Step 1: Visualize the situation
Visualize two parallel fences, 16 ft apart, and the first fence is 2 ft high. We need to find the length of the shortest pole that starts from the ground, passes over the first fence, and reaches the second fence.
Step 2: Determine the height of the second fence
Since the problem states that the second fence is higher than the first, we need to find its height. Unfortunately, the problem does not provide the height of the second fence, so we cannot determine the exact length of the shortest pole.
Step 3: Find the maximum height of the second fence
To minimize the length of the pole, the second fence's height should be as low as possible. Therefore, we can assume the height of the second fence to be zero.
Step 4: Calculate the length of the pole
With the assumption that the second fence's height is zero, we can treat the problem as a right-angled triangle. The distance between the fences (16 ft) serves as the base of the triangle, and the height of the first fence (2 ft) acts as the height of the triangle.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the length of the shortest pole (c).
c^2 = a^2 + b^2
c^2 = 16^2 + 2^2
c^2 = 256 + 4
c^2 = 260
c ≈ √260
c ≈ 16.12 ft
Therefore, the length of the shortest pole that starts from the ground, passes over the first fence (2 ft high), and reaches the second fence (with zero height), is approximately 16.12 ft.