SOLUTION: A vertical stake 20.0cm high cast a horizontal shadow 12.5 cm long. What time is it if the sun rose at 6:00 am and will be directly overhead at noon. I was able to find the adja

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Question 717941: A vertical stake 20.0cm high cast a horizontal shadow 12.5 cm long. What time is it if the sun rose at 6:00 am and will be directly overhead at noon.
I was able to find the adjacent height on the triangle by taking tan theta 20.0/12.5 getting 1.6.
I was then able to fine the angle by taking tan inverse 20.0/12.5 get 57.99 rounding it to 58 degrees.
From there I get stuck. Can you show me each step you take to finishing solving the rest of this problem. Thanks.
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
The sun, as it travels from dawn (horizontal) to noon (vertical) travels through an angle of 90 degrees and it takes 6 hours to do this. Assuming that the angle of the sun changes at a fixed rate will it goes from dawn to noon then the ratio of the angle you found over 90 will be the same as the ratio of how many hours past 6 am it is and 6 (the total time from dawn to noon). So

where x is the number of hours past dawn when the angle is 58 degrees. Now we solve for x. Multiplying by 6:

Since 1/15 of an hour is 4 minutes, x is 58*4 or 232 minutes. This is 3 hours and 52 minutes. Remembering that is how much time past dawn, the time of day when the angle is 58 degrees would be 6 hours + 3 hours and 52 minutes or 9:52 am.