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|Subject Area||Geometry Honors|
|Unit of Instruction||4: Right Triangles and Trigonometry|
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Prove the Law of Sines and Cosines and use them to solve problems.
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
|Learning Targets and Learning Criteria|
I know that I am successful when I can:
- calculate sine and cosine ratios for acute angles in a right triangle when given two side lengths.
- use a diagram of a right triangle to explain that for a pair of complementary angles A and B, the sine of angle A is equal to the cosine of angle B and the cosine of angle A is equal to the sine of angle B.
- solve right triangles by finding the measures of all sides and angles in the triangles using Pythagorean Theorem and/or trigonometric ratios and their inverses.
- draw right triangles that describe real world problems and label the sides and angles with their given measures.
- solve application problems involving right triangles, including angle of elevation and depression, navigation, and surveying.
- derive the Law of Sines by drawing an altitude in a triangle, using the sine function to find two expressions for the length of the altitude, and simplifying the equation that results from setting these expressions equal.
- draw an altitude to create two right triangles and can establish the relationships of the sides in each right triangle using the sine and cosine functions of a single angle in the original triangle.
- derive the Law of Cosines using the Pythagorean Theorem, two right triangles formed by drawing an altitude, and substitution.
- generalize the Law of Cosines to apply to each included angle (a2
- use the Law of Sines and Law of Cosines to solve real world problems.
- use the triangle inequality and side/angle relationships (e.g. largest angle is opposite the largest side) to estimate the measures of unknown sides and angles.
- distinguish between situations that require the Law of Sines (ASA, AAS, SSA) and situations that require the Law of Cosines (SASS, SSS).
- apply the Law of Sines and the Law of Cosines to find unknown side lengths and unknown angle measures in right and non-right triangles.
- use the Law of Sines to determine if two given side lengths and a given non-adjacent angle measures (SSA) make two triangles, one triangle, or no triangle.
Monday (2nd Period) / Tuesday (7th & 8th Periods)
- Bellringer – Pythagorean Theorem, Special Right Triangles (45-45-90) and Trigonometry
- Instruction – Law of Sines and Law of Cosines – Standards MAFS.912.G-SRT.4.10 & MAFS.912.G-SRT.4.11
- Homework – Law of Sines and Law of Cosines Worksheets (ODD PROBLEMS ONLY) – due Thursday, December 14th for 2nd Period and Friday, December 15th for 7th & 8th Periods
Wednesday (All Classes)
- Bellringer – Converse of Pythagorean Theorem, Special Right Triangles (30-60-90), Trigonometry and Angles of Elevation and Depression
- Instruction – Proving Right Triangles Congruent
- Homework – IXL R.13 Solve a triangle – due Wednesday, December 20th for all classes
Thursday (2nd Period) / Friday (7th & 8th Periods)
Unit 4: Right Triangles and Trigonometry Test
Unit 4: Right Triangles and Trigonometry Test – Thursday, December 14th for 2nd Period / Friday, December 15th for 7th & 8th Periods
Worksheets (ONLY DO THE ODD PROBLEMS)
- Angles of Elevation and Depression Worksheets – due Wednesday, December 13th
- R.4 Trigonometric functions of complementary angles – due Monday, December 11th for 2nd Period / Tuesday, December 12th for 7th & 8th Periods
Please refer to the notes in our Geometry Honors course in Canvas on the vPortal for additional resources. In addition, the videos in Geometry Nation are also good sources of information.
The Geometry Nation videos which are beneficial are:
- Section 8, Topic 1: The Pythagorean Theorem
- Section 8, Topic 2: The Converse of the Pythagorean Theorem
- Section 8, Topic 3: Proving Right Triangles Congruent
- Section 8, Topic 4: Special Right Triangles – 45 – 45 – 90
- Section 8, Topic 5: Special Right Triangles – 30 – 60 – 90
- Section 8, Topic 6: Right Triangle Similarity – Part 1
- Section 8, Topic 7: Right Triangle Similarity – Part 2
- Section 8, Topic 8: Trigonometry – Part 1
- Section 8, Topic 9: Trigonometry – Part 2