11 x1 t05 07 angle between two lines
TRANSCRIPT
Angle Between Two Lines
Angle Between Two Linesy
x
Angle Between Two Linesy
x
1l
1
Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m
Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m 2l
2
Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
Angle Between Two Linesy
x
1l
1 2 (exterior ) 1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2 1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2 1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
1 2tan tan
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan
1 tan tan
1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
1 2tan tan
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan
1 tan tan
1
1 1 1 has slope tanl m
1 2
1 21
m m
mm
2l
2
2 2 2 has slope tanl m
1 2tan tan
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan
1 tan tan
1
1 1 1 has slope tanl m
1 2
1 21
m m
mm
2l
2
2 2 2 has slope tanl m
1 2tan tan
The acute angle between two lines with slopes and can be found using;
1m 2m
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan
1 tan tan
1
1 1 1 has slope tanl m
1 2
1 21
m m
mm
2l
2
2 2 2 has slope tanl m
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 1
3y x y x
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 1
3y x y x
31
21
31
2tan
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 1
3y x y x
31
21
31
2tan
2316
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 1
3y x y x
31
21
31
2tan
2316
1
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 1
3y x y x
31
21
31
2tan
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.
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
313
45tan
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
313
45tan
mm
313
1
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
313
45tan
mm
313
1
mm 331
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
313
45tan
mm
313
1
mm 331
mmmm 331 or 331
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
313
45tan
mm
313
1
mm 331
mmmm 331 or 331
24 m
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
313
45tan
mm
313
1
mm 331
mmmm 331 or 331
21m
24 m
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
313
45tan
mm
313
1
mm 331
mmmm 331 or 331
21m
mm 33124 m
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
313
45tan
mm
313
1
mm 331
mmmm 331 or 331
21m
mm 331
42 m
24 m
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
313
45tan
mm
313
1
mm 331
mmmm 331 or 331
21m
mm 331
42 m
2m
24 m
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
313
45tan
mm
313
1
mm 331
mmmm 331 or 331
21m
mm 331
42 m
2m2or
21 mm
24 m
Exercise 14E; 1ac, 2bdf, 4, 7, 8, 10, 11a, 15*