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**+5 **

9 x − y = 3, 8 x + y = 8

y=9x-3, y=-8x+8

m1 = 9 m2=-8

y=9x-3, y=-8x+8

m1 = 9 m2=-8

$${\mathtt{180}}{\mathtt{\,-\,}}{\left|\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{9}}\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(-{\mathtt{8}}\right)}\right|} = {\mathtt{13.465\: \!208\: \!094\: \!812}}$$

like CPhill said about 13 degrees

Melody
Feb 28, 2015

#1**+5 **

9x−y =
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**+5 **

Best Answer

9 x − y = 3, 8 x + y = 8

y=9x-3, y=-8x+8

m1 = 9 m2=-8

y=9x-3, y=-8x+8

m1 = 9 m2=-8

$${\mathtt{180}}{\mathtt{\,-\,}}{\left|\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{9}}\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(-{\mathtt{8}}\right)}\right|} = {\mathtt{13.465\: \!208\: \!094\: \!812}}$$

like CPhill said about 13 degrees

Melody
Feb 28, 2015