Answer:
5.6 = AB
Step-by-step explanation:
Since this is a right triangle, we can use trig functions to find the length of AB
Cos theta = opp side/ hypotenuse
cos 62 = AB / BC
cos 62 = AB /12
Multiply each side by 12
12 cos 62 = AB
5.633658753 = AB
Rounding to 1 decimal place
5.6 = AB
We can also find AC
sin theta = opp side/ hypotenuse
sin 62 = AC / BC
sin 62 = AC /12
Multiply each side by 12
12 sin 62 = AC
10.59537111 = AC
Rounding to 1 decimal place
10.6 = AC
For the last part, you have to find where 
attains its maximum over 
. We have
so that
with critical points at 
such that
So either
or
where 
is any integer. We get 8 solutions over the given interval with 
from the first set of solutions, 
from the set of solutions where 
, and 
from the set of solutions where 
. They are approximately
(50 - (2.75 + 4.25)) / 6 = (50 - 7) / 6 = 43/6 = 7.17 per day
