A cathedral ceiling shown in the figure below 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.
(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? (Round your answer to one decimal place.)
+130536 We can use similar triangles to solve this.
At 3 feet east of the west wall, the ceiling rises 2.5 ft. So....we want to know how far we are from the wall when the ceiling rises 4ft above 8 ft [12 ft is 4ft more than the 8 ft at the wall ] :
3 / 2.5 = d / 4 where d is the distance from the west wall where the ceiling ht = 12ft
Cross-multiply
12 = 2.5 d divide both sides by 2.5
12 / 2.5 = d = 4.8 ft from the west wall
+130536 We can use similar triangles to solve this.
At 3 feet east of the west wall, the ceiling rises 2.5 ft. So....we want to know how far we are from the wall when the ceiling rises 4ft above 8 ft [12 ft is 4ft more than the 8 ft at the wall ] :
3 / 2.5 = d / 4 where d is the distance from the west wall where the ceiling ht = 12ft
Cross-multiply
12 = 2.5 d divide both sides by 2.5
12 / 2.5 = d = 4.8 ft from the west wall
