-a43 points MexTng8 2.2087. My Notes Ask Your Te The Moorish sundial is designed

Question

-a43 points MexTng8 2.2087. My Notes Ask Your Te The Moorish sundial is designed so that the shadow of the gnomon (the vertical triangular plece) is consistent at each hour from one day to the next. This allows the hours to be marked on the sundial using a single scale that is not affected by the changes in the Sun's path during the year. If the sundial is positioned so that the gnomon is aligned along a longitudinal line from north to south, then at exactly noon the gnomon will cast a shadow due north. As the sun moves, the shadow will sweep out an angle toward the east, labeled 8 in the figure above, called the shadow angle. This angle can be calculated using the formula tan 6 - sin a tan(h 15° where is the latitude of the position of the sundial and h is a number of hours from noon. The latitude of a city is 44.286. Find the shadow angle for a sundial in this city at 4:00 p.m. Round to the nearest tenth of a degree. Need Help? T to Titer

Explanation / Answer

tan theta = sin alpha tan(h*15 degree)

alpha =44.286 degree

h=1600 hrs -1200 hrs=4 hrs

tan theta=sin 44.286tan(4*15)

tan theta=sin 44.286 tan 60 degree

tan theta=1.209387828

theta =tan-11.209387828

theta=50.41 degree

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