Question

the ceiling in a hallway 20 feet wide is in the shape of a semi ellipse and 18 ft height at the centre.find the height of the ceiling 4 feet from either wall if the height of the side walls is 12 feet​

Answer 1

Answer:

hope this will help you

Step-by-step explanation:

Let PQR be the height of the ceiling which is 4 feet from the wall. From the diagram PQ = 12 ft To find the height QR

Since the width is 20ft, take A, A′ as vertices with A as (10, 0) and A′ as ( 10, 0). Take the midpoint of AA′ as the centre which is (0, 0)

AA′ = 2a = 20 ⇒ a = 10

and b = 18 12 = 6

∴x2/100 +y2/36 = 1

Let QR be y1 then R is (6, y1) Since R lies on the ellipse,

36/100 +y12/36 = 1 ⇒ y1 = 4.8

∴ PQ + QR = 12 + 4.8

∴ The required height of the ceiling is 16.8 feet