11x1 t08 03 angle between two lines (2010)

Angle Between Two Lines

Angle Between Two Linesy

x


x

1l

1


x

1l

1

1 1 1has slope tanl m


x

1l

1

1 1 1has slope tanl m 2l

2


x

1l

1


2



x

1l

1 2 (exterior ) 1


2



x

1l

1 2 (exterior )

1 2 1


2



x

1l

1 2 (exterior )

1 2 1


2


1 2tan tan


x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan1 tan tan

1


2


1 2tan tan


x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan1 tan tan

1


1 2

1 21m m

m m

2l

2


1 2tan tan


x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan1 tan tan

1


1 2

1 21m m

m m

2l

2


1 2tan tan

The acute angle between two lines with slopes and can be found using;

1m 2m


x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan1 tan tan

1


1 2

1 21m m

m m

2l

2


1 2tan tan

21

21

1tan

mmmm

The acute angle between two lines with slopes and can be found using;

1m 2m

2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines

1 2 1 and 13

y x y x


1 2 1 and 13

y x y x

3121

312

tan


1 2 1 and 13

y x y x

3121

312

tan

2316


1 2 1 and 13

y x y x

3121

312

tan

2316

1


1 2 1 and 13

y x y x

3121

312

tan

2316

145

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.



mm

31345tan



mm

31345tan

mm

3131



mm

31345tan

mm

3131

mm 331



mm

31345tan

mm

3131

mm 331

mmmm 331 or 331



mm

31345tan

mm

3131

mm 331

mmmm 331 or 33124 m



mm

31345tan

mm

3131

mm 331

mmmm 331 or 331

21

m

24 m



mm

31345tan

mm

3131

mm 331

mmmm 331 or 331

21

m

mm 33124 m



mm

31345tan

mm

3131

mm 331

mmmm 331 or 331

21

m

mm 331

42 m

24 m



mm

31345tan

mm

3131

mm 331

mmmm 331 or 331

21

m

mm 331

42 m

2m

24 m



mm

31345tan

mm

3131

mm 331

mmmm 331 or 331

21

m

mm 331

42 m

2m2or

21

mm

24 m

Exercise 14E; 1ac, 2bdf, 4, 7, 8, 10, 11a, 15*

11x1 t08 03 angle between two lines (2010)

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