Problema Solution
two vertical poles of lengths 8 feet and 11 feet stand 14 feet apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. Where should this point be located to use 25 feet of cable?
Answer provided by our tutors
Let x be the distance from the 8 foot pole to the anchor.
Then 14 – x is the distance from the anchor to the 11 foot pole.
Let d be the segment of the cable from the 8 foot pole to the anchor.
Let m be the segment of the cable from the 11 foot pole to the anchor.
Then, according to the statement of the problem, d + m = 25.
Application of the Pythagorean Theorem to the obvious two triangles yields:
d^2 = x^2 + 8^2
d = (x^2 + 8^2)^0.5
m^2 = (14 - x)^2 + 11^2
m = ((14 - x)^2 + 11^2)^0.5
d + m = 25
(x^2 + 8^2)^0.5 + ((14 - x)^2 + 11^2)^0.5 = 25
by solving we find:
x = 36.45 ft
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the point should be 36.45 ft from the 8 foot pole.