Chapter 3.1, Problem 15E

Reminder Round all answers two decimals places unless otherwise indicated.

A Cathedral Ceiling A cathedral ceiling shown in Figure $3.18$ is $8$ feet high at the west wall of a room. As you go from the west wall toward the east wall the ceiling slants upward. Three feet from the west wall, the ceiling is $10.5$ feet high.

a. What is the slope of the ceiling?

b. The width of the room (the distance from the west wall to the east wall) is $17$ feet. How high is the ceiling at the east wall?

c. You want to install a light in the ceiling as far away from the west wall as possible. You intend to change the bulb, when required, by standing near the top of your small stepladder. If you stand on the highest safe step of your stepladder, you can reach $12$ feet high. How far from the west wall should you install the light?