The document discusses trigonometry concepts related to 3D shapes and solving problems involving angles of elevation. Specifically:
- When doing 3D trigonometry, it is often useful to redraw shapes in 2D to analyze them.
- A worked example problem is shown to find the distance and bearing between a life raft (David's position) and a search vessel (Anna's position) based on angles of elevation they each observe of a mountain peak.
- Applying trigonometric relationships involving angles and the mountain's known height, the distance between David and Anna is calculated to be 2799 meters, and the bearing of David from Anna is calculated to be 249°51'.
Maths project --some applications of trignometry--class 10Mahip Singh
Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.
The data is present below the pictures so as to edit it as per your needs. I wanted to use good fonts and this was the only way i could do it as the fonts would not be available on your computer.
Maths project --some applications of trignometry--class 10Mahip Singh
Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.
The data is present below the pictures so as to edit it as per your needs. I wanted to use good fonts and this was the only way i could do it as the fonts would not be available on your computer.
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http://sandymillin.wordpress.com/iateflwebinar2024
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2. 3D Trigonometry
When doing 3D trigonometry it is often useful to redraw all of the
faces of the shape in 2D.
3. 3D Trigonometry
When doing 3D trigonometry it is often useful to redraw all of the
faces of the shape in 2D.
2003 Extension 1 HSC Q7a)
David is in a life raft and Anna is in a cabin cruiser searching for him.
They are in contact by mobile phone. David tells Ana that he can see
Mt Hope. From David’s position the mountain has a bearing of 109 ,
and the angle of elevation to the top of the mountain is 16.
Anna can also see Mt Hope. From her position it has a bearing of 139,
and and the top of the mountain has an angle of elevation of 23 .
The top of Mt Hope is 1500 m above sea level.
Find the distance and bearing of the life raft from Anna’s position.
19. H H
1500 m N’ 1500 m
16 23
D B A B
A 139
N
b
1500 tan 67 N”
D
109 30
1500 tan 74
B
20. b 2 1500 2 tan 2 67 1500 2 tan 2 74 2 1500 tan 67 1500 tan 74 cos 30
21. b 2 1500 2 tan 2 67 1500 2 tan 2 74 2 1500 tan 67 1500 tan 74 cos 30
b 2798.96
2799 (to nearest metre)
Anna and David are 2799 m apart.
22. H H
1500 m N’ 1500 m
16 23
D B A B
A 139
N
b
1500 tan 67 N”
D
109 30
1500 tan 74
B
23. b 2 1500 2 tan 2 67 1500 2 tan 2 74 2 1500 tan 67 1500 tan 74 cos 30
b 2798.96
2799 (to nearest metre)
Anna and David are 2799 m apart.
sin DAB sin 30
1500 tan 74 b
24. b 2 1500 2 tan 2 67 1500 2 tan 2 74 2 1500 tan 67 1500 tan 74 cos 30
b 2798.96
2799 (to nearest metre)
Anna and David are 2799 m apart.
sin DAB sin 30
1500 tan 74 b
1500 tan 74 sin 30
sin DAB
b
DAB 699' or 11051'
25. b 2 1500 2 tan 2 67 1500 2 tan 2 74 2 1500 tan 67 1500 tan 74 cos 30
b 2798.96
2799 (to nearest metre)
Anna and David are 2799 m apart.
sin DAB sin 30
1500 tan 74 b
1500 tan 74 sin 30
sin DAB
b
DAB 699' or 11051'
If DAB 699'
then BDA 8051'
26. b 2 1500 2 tan 2 67 1500 2 tan 2 74 2 1500 tan 67 1500 tan 74 cos 30
b 2798.96
2799 (to nearest metre)
Anna and David are 2799 m apart.
sin DAB sin 30
1500 tan 74 b
1500 tan 74 sin 30
sin DAB
b
DAB 699' or 11051'
If DAB 699'
then BDA 8051'
But DAB BDA
BDA 11051'
27. H H
1500 m N’ 1500 m
16 23
D B A B
A 139
N
b 11051'
1500 tan 67 N”
D
109 30
1500 tan 74
B
28. b 2 1500 2 tan 2 67 1500 2 tan 2 74 2 1500 tan 67 1500 tan 74 cos 30
b 2798.96
2799 (to nearest metre)
Anna and David are 2799 m apart.
sin DAB sin 30
1500 tan 74 b
1500 tan 74 sin 30
sin DAB
b
DAB 699' or 11051'
If DAB 699'
then BDA 8051'
But DAB BDA
BDA 110 51'
The bearing of David from Anna is 24951'
29. 2000 Extension 1 HSC Q3c)
A surveyor stands at point A, which is due south of a tower OT of
height h m. The angle of elevation of the top of the tower from A is 45
The surveyor then walks 100 m due east to point B, from where she
measures the angle of elevation of the top of the tower to be 30
31. (i) Express the length of OB in terms of h.
T
h
30
0 B
OB
tan 60
h
OB h tan 60
32. (i) Express the length of OB in terms of h.
T
h
30
0 B
OB
tan 60
h
OB h tan 60
(ii) Show that h 50 2
33. (i) Express the length of OB in terms of h.
T
h
30
0 B
OB
tan 60
h
OB h tan 60
(ii) Show that h 50 2
T
h
A 45 0
34. (i) Express the length of OB in terms of h.
T
h
30
0 B
OB
tan 60
h
OB h tan 60
(ii) Show that h 50 2
T
h
A 45 0
ATO is isosceles
AO h
35. (i) Express the length of OB in terms of h.
T
h
30
0 B
OB
tan 60
h
OB h tan 60
(ii) Show that h 50 2
T O
h h tan 60
h
A 45 0 A B
100
ATO is isosceles
AO h
36. (i) Express the length of OB in terms of h.
T
h
30
0 B
OB
tan 60
h
OB h tan 60
(ii) Show that h 50 2
T O h 2 100 2 h 2 tan 2 60
h h tan 60
h
A 45 0 A B
100
ATO is isosceles
AO h
37. (i) Express the length of OB in terms of h.
T
h
30
0 B
OB
tan 60
h
OB h tan 60
(ii) Show that h 50 2
T O h 2 100 2 h 2 tan 2 60
h h tan 60 h 2 100 2 3h 2
h
45 2h 2 100 2
A 0 A B 100 2
100 h
2
ATO is isosceles 2
100
AO h h
2
h 50 2
39. (iii) Calculate the bearing of B from the base of the tower.
N
O
50 2
A 100 B
40. (iii) Calculate the bearing of B from the base of the tower.
N
100
tan AOB
50 2
O
50 2
A 100 B
41. (iii) Calculate the bearing of B from the base of the tower.
N
100
tan AOB
50 2
AOB 54 44'
O
50 2
A 100 B
42. (iii) Calculate the bearing of B from the base of the tower.
N
100
tan AOB
50 2
AOB 54 44'
O
bearing 180 54 44'
50 2 12516'
A 100 B
43. (iii) Calculate the bearing of B from the base of the tower.
N
100
tan AOB
50 2
AOB 54 44'
O
bearing 180 54 44'
50 2 12516'
A 100 B
Book 2: Exercise 2G odds
Exercise 2H evens