SOLUTION: A tree on top of a hill casts a shadow of 20 m long down the hill. Of the angle of elevation of the sun is 75 degrees and the hill is inclined 45 degrees, find the height of the t

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Question 827668: A tree on top of a hill casts a shadow of 20 m long down the hill. Of the angle of elevation of the sun is 75 degrees and the hill is inclined 45 degrees, find the height of the tree
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
RS = 20 m = shadow of tree
Consider right triangle RSP.
PS=RS%2Acos%2845%5Eo%29=%2820m%29%28sqrt%282%29%2F2%29=14.14m (rounded to nearest 0.1m)
RP=RS%2Asin%2845%5Eo%29=%2820m%29%28sqrt%282%29%2F2%29=14.14m (rounded to nearest 0.1m)
Consider right triangle TSP.
PT=PS%2Atan%2875%5Eo%29=%2814.14m%29%2A3.732=52.78m (rounded to nearest 0.1m)
The height of the tree is
RT=PT-RP=52.78m-14.14m=38.64m (rounded to nearest 0.1m).
(Maybe it should be rounded to 39 meters, since the shadow's length and angles do not seem to have been measured with such fine precision).