11x1 t08 03 angle between two lines (2010)
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![Page 1: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/1.jpg)
Angle Between Two Lines
![Page 2: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/2.jpg)
Angle Between Two Linesy
x
![Page 3: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/3.jpg)
Angle Between Two Linesy
x
1l
1
![Page 4: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/4.jpg)
Angle Between Two Linesy
x
1l
1
1 1 1has slope tanl m
![Page 5: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/5.jpg)
Angle Between Two Linesy
x
1l
1
1 1 1has slope tanl m 2l
2
![Page 6: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/6.jpg)
Angle Between Two Linesy
x
1l
1
1 1 1has slope tanl m 2l
2
2 2 2has slope tanl m
![Page 7: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/7.jpg)
Angle Between Two Linesy
x
1l
1
1 1 1has slope tanl m 2l
2
2 2 2has slope tanl m
![Page 8: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/8.jpg)
Angle Between Two Linesy
x
1l
1 2 (exterior ) 1
1 1 1has slope tanl m 2l
2
2 2 2has slope tanl m
![Page 9: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/9.jpg)
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2 1
1 1 1has slope tanl m 2l
2
2 2 2has slope tanl m
![Page 10: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/10.jpg)
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2 1
1 1 1has slope tanl m 2l
2
2 2 2has slope tanl m
1 2tan tan
![Page 11: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/11.jpg)
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan1 tan tan
1
1 1 1has slope tanl m 2l
2
2 2 2has slope tanl m
1 2tan tan
![Page 12: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/12.jpg)
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan1 tan tan
1
1 1 1has slope tanl m
1 2
1 21m m
m m
2l
2
2 2 2has slope tanl m
1 2tan tan
![Page 13: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/13.jpg)
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan1 tan tan
1
1 1 1has slope tanl m
1 2
1 21m m
m m
2l
2
2 2 2has slope tanl m
1 2tan tan
The acute angle between two lines with slopes and can be found using;
1m 2m
![Page 14: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/14.jpg)
Angle Between Two Linesy
x
1l
1 2 (exterior )
1 2
1 2
1 2
tan tan1 tan tan
1
1 1 1has slope tanl m
1 2
1 21m m
m m
2l
2
2 2 2has 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
![Page 15: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/15.jpg)
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 13
y x y x
![Page 16: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/16.jpg)
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 13
y x y x
3121
312
tan
![Page 17: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/17.jpg)
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 13
y x y x
3121
312
tan
2316
![Page 18: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/18.jpg)
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 13
y x y x
3121
312
tan
2316
1
![Page 19: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/19.jpg)
2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 13
y x y x
3121
312
tan
2316
145
![Page 20: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/20.jpg)
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.
![Page 21: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/21.jpg)
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
![Page 22: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/22.jpg)
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
3131
![Page 23: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/23.jpg)
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
3131
mm 331
![Page 24: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/24.jpg)
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
3131
mm 331
mmmm 331 or 331
![Page 25: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/25.jpg)
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
3131
mm 331
mmmm 331 or 33124 m
![Page 26: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/26.jpg)
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
3131
mm 331
mmmm 331 or 331
21
m
24 m
![Page 27: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/27.jpg)
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
3131
mm 331
mmmm 331 or 331
21
m
mm 33124 m
![Page 28: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/28.jpg)
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
3131
mm 331
mmmm 331 or 331
21
m
mm 331
42 m
24 m
![Page 29: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/29.jpg)
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
3131
mm 331
mmmm 331 or 331
21
m
mm 331
42 m
2m
24 m
![Page 30: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/30.jpg)
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
3131
mm 331
mmmm 331 or 331
21
m
mm 331
42 m
2m2or
21
mm
24 m
![Page 31: 11X1 T08 03 angle between two lines (2010)](https://reader034.vdocuments.us/reader034/viewer/2022051209/5481115a5806b506118b4611/html5/thumbnails/31.jpg)
Exercise 14E; 1ac, 2bdf, 4, 7, 8, 10, 11a, 15*