Question 188351: a tree is 66 meters high casts a 44 meter shadow. find the angle of elevation of the sun. Found 2 solutions by stanbon, aggie_tutor:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! a tree is 66 meters high casts a 44 meter shadow. find the angle of elevation of the sun.
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Draw the picture ; put the sun in the picture.
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tan(angle of elevation) = 66/44
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angle of elevation = arctan(66/44) = 56.31 degrees
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Cheers,
Stan H.
You can put this solution on YOUR website! +++++
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...44
a=66
b=44
Angle A is the sought angle. Since you know the a and b sides, use arctangent (inverse tan).
tan A = a/b
tan A = 66/44 = 1.5
now arctan the result to get the angle.
(inv tan)1.5 = 56.31 (rounded up)
Check your answer: all angles in the triangle add up to 180. The right triangle has a 90 degree angle, so 180-90-56.31 = 33.69 should be the other unsolved angle.
tan B = b/a
tan B = 44/66 = .6667
(inv tan).6667 = 33.69
Geometry purist may want to post a proof that does not use trig funcs.
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