Chapter 6.1, Problem 66PE

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 $23.5°\text{N}$ will see the Sun directly overhead at noon. Points on the Earth with latitude $23.5°\text{N}$ are on the Tropic of Cancer. Key West, Florida, has latitude $24.6°{\rm N}$ , 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 $105\text{-ft}$ 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 $40\text{-ft}$ tree at noon on the first day of fall or spring.