The number of daylight hours H at any location can be calculated by using the fo
ID: 3108973 • Letter: T
Question
The number of daylight hours H at any location can be calculated by using the formula
cos(0.1309H)= -tan D tan L
where L is the latitude of the location on Earth, and D is the declination of the sun (which varies because
the Earth is tilted on its axis). Minneapolis, Minnesota has a latitude of 44.88 degrees
a. Calculate the length of a day in Minneapolis when D= 11.11 degrees. Round your answer
to the nearest tenth of an hour.
b. Calculate the length of a day in Minneapolis when D = 0 degrees. Round your answer
to the nearest whole hour. Does this answer make sense? Why or why not?
Explanation / Answer
Given:
cos(0.1309 H) = - tan D tan L (1)
(a) Given:
L = 44.88 degrees
D = 11.11 degrees
Substituting, (1) becomes:
cos (0.1309 H) = - tan 11.11 tan 44.88
= - 0.1964 X 0.9958
= - 0.1956
So,
0.1309 H = cos-1 (- 0.1956)
= 1.7677
So,
H = 13.50
(b) Given:
L = 44.88
D = 0
cos(0.1309 H) = - tan D tan L
= - tan 0 tan 44.88
= 0
0.1309 H = cos-1 0 = 1.5706
So,
H = 1.5708/0.1309 = 12.0