Posted by alex on Tuesday, July 19, 2011 at 11:01am.
We need to form 2 rt triangles with a common ver. side.
First, draw a rectangle with the long
side parallel to the x-axis. Then draw
a diagonal from the lower Lt corner to
the upper rt corner. This is the hyp
of the larger triangle. From a point near the center of the hor side, draw
another hyp to the upper rt corner. This is the hyp of the smaller
The angle bet. the hyp of larger tri-
angle and hor is 40 deg. The 60-degree
angle is bet hyp and hor of smaller triangle.
The dist. bet. the 2 hyp is 200 ft Label the remaining dist. X ft and the
ver side is h for ht of tree.
Width = 200 + X.
tan60 = h/x,
h = xtan60.
tan40 = h/(200+x),
h = (x+200)tan40.
xtan60 = (x+200)tan40,
xtan60 = xtan40 + 200tan40,
xtan60 - xtan40 = 200tan40,
1.732x - 0.8391x = 167.82,
0.8929x = 167.82,
X = 188.
Width = 200 + 188 = 388 Ft.
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