Question 514169: A tree on a hillside casts a shadow c ft down the hill. If the angle of inclination of the hillside is b to the horizontal and the angle of elevation of the sun is a, find the height of the tree. Assume a = 57°, b = 27° c = 220 ft
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A tree on a hillside casts a shadow c ft down the hill. If the angle of inclination of the hillside is b to the horizontal and the angle of elevation of the sun is a, find the height of the tree. Assume a = 57°, b = 27° c = 220 ft
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From point(A) draw a line 27º to the horizontal representing the hill.
On the hill 220 ft from point A, draw a vertical line(h) representing the tree.
From point(A) draw a line 57º to the horizontal to the top of the tree.
From the bottom of the tree, extend a vertical line(y) down to a point on the horizontal.
x=distance from point A to where line(y) intersects with the horizontal
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x/220=cos 27º
x=220 cos 27º=196.02
..
y/x=tan 27º
y=x tan 27º
y=196.02 tan 27º=99.88
..
(h+y)/x=tan 57º
h+y=x tan 57º=301.84
h=301.84-99.8=202.04 ft
..
ans:
height of tree≈202 ft
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