Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u07-l06', 'number': 6, 'title': 'Periodic and Triangle Models in Context', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
In a right triangle, opposite=6 and hypotenuse=10. Find sin θ.
2. {'id': 'u07-l06', 'number': 6, 'title': 'Periodic and Triangle Models in Context', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Given a=7, A=35°, B=62°, find angle C.
3. {'id': 'u07-l06', 'number': 6, 'title': 'Periodic and Triangle Models in Context', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Which law fits SAS data?
4. {'id': 'u07-l06', 'number': 6, 'title': 'Periodic and Triangle Models in Context', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Find c when a=5, b=8, C=60°.
5. {'id': 'u07-l06', 'number': 6, 'title': 'Periodic and Triangle Models in Context', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Find the area with a=10, b=12, C=30°.
6. {'id': 'u07-l06', 'number': 6, 'title': 'Periodic and Triangle Models in Context', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
A bearing of N35°E corresponds to what standard compass description?
7. {'id': 'u07-l07', 'number': 7, 'title': 'Measurement Error, Precision & Model Defense', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
In a right triangle, opposite=6 and hypotenuse=10. Find sin θ.
8. {'id': 'u07-l07', 'number': 7, 'title': 'Measurement Error, Precision & Model Defense', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Given a=7, A=35°, B=62°, find angle C.
9. {'id': 'u07-l07', 'number': 7, 'title': 'Measurement Error, Precision & Model Defense', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Which law fits SAS data?
10. {'id': 'u07-l07', 'number': 7, 'title': 'Measurement Error, Precision & Model Defense', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Find c when a=5, b=8, C=60°.
11. {'id': 'u07-l07', 'number': 7, 'title': 'Measurement Error, Precision & Model Defense', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
Find the area with a=10, b=12, C=30°.
12. {'id': 'u07-l07', 'number': 7, 'title': 'Measurement Error, Precision & Model Defense', 'family': 'triangles', 'week': 22, 'unit': 7, 'unit_title': 'Triangle Trigonometry, Bearings & Applications', 'essential': 'How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?', 'project': 'Navigation, Survey & Triangulation Field Study'}
A bearing of N35°E corresponds to what standard compass description?