Answer:
15th February.
Step-by-step explanation:
We have to solve the equation [tex]h = 3.98 \sin 2\pi \frac{n-80}{365} +12.16[/tex] for the value of h = 10 hours.
Now, [tex]10 = 3.98 \sin 2\pi \frac{n-80}{365} +12.16[/tex]
⇒[tex]3.98 \sin 2\pi \frac{n-80}{365} =-2.16[/tex]
⇒[tex]\sin 2\pi \frac{n-80}{365} = -0.5427[/tex]
⇒ [tex]2\pi \frac{n-80}{365} = \sin^{-1}(-0.5427) =-32.868 = -0.1826\pi[/tex]
{Since π = 180°}
⇒ [tex]\frac{n-80}{365} = -0.913[/tex]
⇒ n - 80 = - 33.325
⇒ n = 46.6749
Therefore, at the 46th day of the year i.e. (46 - 31) = 15th February there should be about 10 hours of day light. (Answer)
