The number of daylight hours H at any location can be calculated by using the fo

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

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