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We have 2 poles 5 m and 7 m height ropes are connected from
top of one to tthe bottem of another find the intersection
height of those poles.
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Answer Posted / jagdeep
two poles of 5m and 7m respetively. a wire is tied from top
of one to bottom of other. at what heightthe two wires will
cross
We will use algebra and an x-y coordinate axis to solve this
problem. Let the pole of 5 m be located at the origin, so
the two ends of that pole are at (0,0) and (0,5). Let the
pole of 7 m be located on the x-axis at a distance of a to
the right of the first pole, so the two ends of that pole
are at (a, 0) and (a,7). The problem does not state the
distance between the poles, so we let that equal an unknown
constant "a" for now. We will find out later that the value
of "a" is irrelevant.
So we want to draw two lines, one from the base of one to
the top of the other and vice versa.
Line 1: Points (0,0) and (a,7)
Slope of line 1: m = 7/a
Intercept of line 1: b = 0
Equation of line 1: y = (7/a) x
Line 2: Points (0,5) and (a,0)
Slope of line 2: m=-5/a
Intercept of line 2: b = 5
Equation of line 2: y = (-5/a)x + 5
The point where these lines meet is the place where the
wires cross!
Solve equation 1 for x:
x = (a/7) y
Substitute this into equation 2:
y = (-5/a) (a/7) y + 5
Notice that a cancels out!
y = (-5/7)y + 5
(12/7) y = 5
12y = 35
y = 35/12 = 2.912
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