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# Find the acute angle between the lines. Round your answer to the nearest degree.

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Find the acute angle between the lines. Round your answer to the nearest degree.

9 x y = 3,      8 x + y = 8
Guest Feb 27, 2015

#2
+92256
+5
9 x y = 3,      8 x + y = 8
y=9x-3,             y=-8x+8

m1 = 9                 m2=-8

$${\mathtt{180}}{\mathtt{\,-\,}}{\left|\underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{9}}\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(-{\mathtt{8}}\right)}\right|} = {\mathtt{13.465\: \!208\: \!094\: \!812}}$$

like CPhill said  about  13 degrees
Melody  Feb 28, 2015
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#1
+85958
+5
9xy = 3,     8x + y = 8

Let's find the slope of each line

y = 9x - 3         y = -8 + 8

And the slope of the first line is 9

And the slope of the second line is -8

And taking the tangent inverse of the second line, we have

tan-1(-8)  = -82.87°   We need to add 180° to this to get the correct angle = 97.13°

And taking the tangent inverse of the first line, we have

tan-1(9) = 83.66°

So.....subtrating the second result from the first, we have 13.47° = about 13°

CPhill  Feb 28, 2015
#2
+92256
+5
$${\mathtt{180}}{\mathtt{\,-\,}}{\left|\underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{9}}\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(-{\mathtt{8}}\right)}\right|} = {\mathtt{13.465\: \!208\: \!094\: \!812}}$$