SOLUTION: A vertical stake 77.0 cm high casts a horizontal shadow 50.0 cm long. What time is it if the sun was directly overhead at 12:30 pm and will set at 6:30 pm? Please walk me throu

Question 809473: A vertical stake 77.0 cm high casts a horizontal shadow 50.0 cm long. What time is it if the sun was directly overhead at 12:30 pm and will set at 6:30 pm?
Please walk me through EACH individual step. I'm more concerned with the proceess than the answer.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A vertical stake 77.0 cm high casts a horizontal shadow 50.0 cm long. What time is it if the sun was directly overhead at 12:30 pm and will set at 6:30 pm?
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In 6 hours the from 12:30 to 6:30, the sun will rotate 90˚.
The elapsed time will be proportional to the degrees the sun rotated from 0˚at 12:30.
The degree the sun rotated is equal to the angle for which the tan=50/77 or
arctan(50/77)=33˚. This is the angle the pole makes with the hypotenuse of the right triangle formed by the 77 ft pole and its 50 ft shadow.
Time elapsed=33/90*6=2.2 hrs
Time=2:32.2 PM
Sorry, I don't have the means to draw a diagram for you.
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