Final answer:
By applying the 1/4 ratio and using the Pythagorean theorem, it can be determined that Dr. Duvernay Tardif's 17 foot ladder will be able to reach a window 16 feet off the ground while maintaining the safety ratio.
Step-by-step explanation:
To determine if Dr. Duvernay Tardif's 17 foot ladder will reach a window 16 feet off the ground using a 1/4 ratio, we need to calculate the height the ladder will reach when it is placed according to this ratio. The 1/4 ratio means that for every 4 feet of height, the base of the ladder should be 1 foot away from the structure. To ensure safety and stability, the ladder's angle of elevation should be such that the base of the ladder is one-quarter of the ladder's working length away from the wall.
To find out the maximum height the ladder can reach at this angle, we can use the Pythagorean theorem. In this setup, the ladder forms the hypotenuse of a right-angled triangle, with the ground and the wall of the building forming the other two sides. By setting up the equation with the ladder's length (L) being 17 feet, and the distance from the wall (D) being 1/4th of the height reached (H), we use the formula L^2 = D^2 + H^2.
Assuming the base is placed 1 foot away for every 4 feet of height, D will be H/4. Therefore, substituting D with H/4 in the formula, we get:
17^2 = (H/4)^2 + H^2
Solving for H, it can then be determined that the ladder will safely reach the window, provided that the ladder is indeed long enough when applying this ratio to reach the 16 feet height required.