solve the problem for a person of height zero, then add 5 feet to the answer. Also assume his eyes are on the top of his head.
If he starts at distance x, and the tower has height h, then
h/x = tan 30
h/(x-425) = tan 58
eliminate x to get
h/tan30 = h/tan58 + 425
now just solve for h.
This is easy problem if you draw the triangles properly.
If we consider the height of the tower above the person to be x and the distance remaining to reach the tower from where he made the last measurement to be y then
tan 32 = y/x
0.625 = y/x
x = y/0.625 = 1.6 y
but we also know from the larger triangle (the starting point) that
tan 30 = x/(425+y)
0.577 = x/(425+y)
x = 245.37 + 0.577 y
substitute from first equation into second one
1.6 y = 245.37 + 0.577 y
1.023 y = 245.37
y = 245.37/1.023= 239.85 feet
x = 1.6 * 239.85 = 383.76 feet
the height of the tower = 5 + 383.76= 388.76 feet
Thank you so much for the help.
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