For Exercises 65-66, refer to the table giving the angle of the Sun at noon at the first day of each season based on the latitude of the observer in the northern hemisphere. The term 23.5 ° represents the tilt of the Earth to the ecliptic plane (plane of the Earth's orbit around the Sun). The Earth is tilted 23.5 ° on its axis. Therefore, at noon on the summer solstice, the Earth is tilted 23.5 ° toward the Sun and all points on the Earth with latitude 23.5 ° N will see the Sun directly overhead at noon. Points on the Earth with latitude 23.5 ° N are on the Tropic of Cancer. Key West, Florida, has latitude 24.6 ° Ν , just above the Tropic of Cancer. a. Find the angle of elevation of the Sun at noon in Key West on the first day of summer and on the first day of winter. b. Find the length of a shadow cast by a 105 -ft building at noon on the first day of summer and on the first day of winter. Round to the nearest tenth of a foot. c. Find the length of a shadow cast by a 40 -ft tree at noon on the first day of fall or spring.
For Exercises 65-66, refer to the table giving the angle of the Sun at noon at the first day of each season based on the latitude of the observer in the northern hemisphere. The term 23.5 ° represents the tilt of the Earth to the ecliptic plane (plane of the Earth's orbit around the Sun). The Earth is tilted 23.5 ° on its axis. Therefore, at noon on the summer solstice, the Earth is tilted 23.5 ° toward the Sun and all points on the Earth with latitude 23.5 ° N will see the Sun directly overhead at noon. Points on the Earth with latitude 23.5 ° N are on the Tropic of Cancer. Key West, Florida, has latitude 24.6 ° Ν , just above the Tropic of Cancer. a. Find the angle of elevation of the Sun at noon in Key West on the first day of summer and on the first day of winter. b. Find the length of a shadow cast by a 105 -ft building at noon on the first day of summer and on the first day of winter. Round to the nearest tenth of a foot. c. Find the length of a shadow cast by a 40 -ft tree at noon on the first day of fall or spring.
For Exercises 65-66, refer to the table giving the angle of the Sun at noon at the first day of each season based on the latitude of the observer in the northern hemisphere. The term
23.5
°
represents the tilt of the Earth to the ecliptic plane (plane of the Earth's orbit around the Sun).
The Earth is tilted
23.5
°
on its axis. Therefore, at noon on the summer solstice, the Earth is tilted
23.5
°
toward the Sun and all points on the Earth with latitude
23.5
°
N
will see the Sun directly overhead at noon. Points on the Earth with latitude
23.5
°
N
are on the Tropic of Cancer. Key West, Florida, has latitude
24.6
°
Ν
, just above the Tropic of Cancer.
a. Find the angle of elevation of the Sun at noon in Key West on the first day of summer and on the first day of winter.
b. Find the length of a shadow cast by a
105
-ft
building at noon on the first day of summer and on the first day of winter. Round to the nearest tenth of a foot.
c. Find the length of a shadow cast by a
40
-ft
tree at noon on the first day of fall or spring.
Suppose a boat leaves port, travels 7 kilometers, turns 21°, and then travels another 12 kilometers. How far is the boat from the port? Start by drawing a diagram.
Calculate the declination and right ascension of the
sun when it is at longitude 90° (summer solstice) and
longitude 45°. By symmetry, find the declination at
longitudes 270° and 315°.
The Eiffel tower is 970 feet talle If the shadow
iS 1200 feet lang at 11:00 am, what is the angle
of elevation to the top Of the tower qt the time
of day.
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