Final answer:
Using the 1:4 safety ratio, the base of a 17-ft ladder needs to be 4 ft from a structure for it to safely reach a 16 ft height. After calculations using the Pythagorean theorem, such a ladder would be capable of safely reaching the window.
Step-by-step explanation:
Dr. Duvernay-Tardif wants to use a 17-ft ladder to reach a window 16 ft off the ground, maintaining a one-for (1:4) ratio for the distance from the ladder base to the structure compared to the height the ladder reaches. To determine if the ladder will reach the window, we'll use the Pythagorean theorem for right triangles, where the ladder serves as the hypotenuse, and the ground-to-structure distance is the adjacent side.
According to the 1:4 ratio, for every 4 feet of height reached, the base of the ladder must be 1 foot from the structure. Therefore, if the window is 16 ft high, the ladder base should be 16 ft / 4 = 4 ft from the structure to maintain the safety ratio.
Using the Pythagorean theorem, a² + b² = c², where 'a' is the distance from the structure, 'b' is the height reached, and 'c' is the length of the ladder. With 'a' as 4 ft and 'b' as 16 ft, we have:
4² + 16² = c²
16 + 256 = c²
272 = c²
c = √272
c ≈ 16.5 ft
Since the ladder needs to be approximately 16.5 ft to reach the window safely while maintaining the 1:4 ratio and Dr. Duvernay-Tardif has a 17-ft ladder, it will indeed reach the window.