How do I solve this?

Step-by-step explanation:

Just so that we have something to work with, the length of the longest day (June 22) in Acron Ohio is 15 hours 8 minutes and 9 seconds on the 20th of June of this year. The number we get won't be this accurate, but it will tell us if we have done it correctly. The tricky part is when to use the radians.

cos(0.1309 H) = -0.4336 tan (40o 46 minutes)  I have assumed this is in radians. It won't work any other way. The measurement cannot be in degrees which will give a negative tan from the minus sign out in front. The cos being minus will make things even worse.

cos(0.1309 H) = -0.4336 tan (40 46/60  )

cos(0.1309 H) = -0.4336 tan (40.766666667)

cos(0.1309 H) = -0.4336 * -0.074173405

cos(0.1309 H) = 0.032161588

0.1309 H = cos-1(0.032161588)

0.1309 H =  1.538629191

H = 1.538629191 / 0.1309

H = 11.754 which is no where near 15 hours, but it is what the numbers give.

I would suggest that you go to your instructor for the other two. Work this one out until you get somewhere near 11.7 hours.

The other two cities should come to something near  this answer.