Re: need help on a geom formula
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Re: need help on a geom formula
Scott Wolf writes:
>Does anyone know the formula for finding the measurement of an angle when
>the slope of the two lines is known. I know it has something to do with
>sin^-1 but my math teacher can't figure out.
>
>Thanks in advance.
>Scott Wolf
>
Several people have provided parts of the answer here. Everything stems from
the fact that the slope of a line in the coordinate plane is given by m =
tan(@) , where @ (theta) is the measure (positive or negative) of the acute
angle the line makes with the positive x-axis. This comes from the definition
of slope as the ratio of delta-y to delta-x. The slope of a vertical line is
undefined (as is the tangent of a right angle measure).
Therefore @ = arctan(m), where arctan is the inverse tangent function
(available on the TI calcs as 2nd tan). if you are given two slopes m1 and m2
for two different lines, the positive angle between the lines will measure
abs(arctan(m1)-arctan(m2)). By applying the addition formula for the tangent
function you can transform this into the formula given by Dawson Wong. Of
course, the transformed formula will not apply if m1*m2 = -1 (if the two given
lines are perpendicular), which just might happen.
Getting rid of all these special cases (vertical lines, perpendiculars, etc.)
can be taken care of by moving up to more general systems of coordinates
(advanced analytic geometry), but most people prefer just to suffer with them.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
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