Chapter 6.1, Problem 65PE

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).

In 1987, a group of protesters lead by Jacqueline kennedy Onassis defeated a plan to build two high rises that would have blocked sunlight to a significant swath of New York City’s Central Park. Eventually the design was scaled down and the buildings height reduced from appropriately 1020 ft to what is now the Time Warner Center at 750 ft.

a. The latitude of New York City is $40.7°\text{N}$ . Find the angle of elevation of the Sun at noon on the winter solstice (shortest day of the year).

b. At noon on the winter solstice, how long is the shadow cast by a $1020\text{-ft}$ building?

c. At noon on the winter solstice, how long is the shadow cast by a $750\text{-ft}$ building?