Question

On a sunny day, a 30-m tall flag pole and its shadow form the sides of a right triangle. On this particular day, the sun rises at 6 AM and sets at 6 PM. At what time of the morning (to the nearest minute) will the length of the shadow be exactly 40 m? (Hint: determine the angle of elevation of the sun)

Answer 1

I'm not completely sure on this one, but hopefully it's correct.
\[\tan^{-1} (30/40)= \angle sun\]=36.87º
The sunlight lasts for twelve hours (6 AM to 6 PM), and in that period of time it travels 180º. Therefore:
180º/12 hours= 15º per hour
36.87º/(15º per hour)=2.45799 hours
This is equivalent to 2 hours + .45799 hours.
6AM+ 2 hrs + .45799 hrs = 8AM +.45799 hrs
\[.45799 hrs \times 60 \min \approx 27 \min\]
8AM + 27 min= 8:27 AM

Answer 2

thank you :)