# Basic Trig

**Essential Question: How can you find the length of a side of a triangle or the measure of any angle?**

**Angles**

**1) Measuring an Angle with Degrees, Minutes, and Seconds**

- Explanation:
- Practice Problems:
- Worksheet #2

**Basic Trig**

**2) Introduction to Trig Ratios**

- Explanation:
- Notes | Annotated
- Khan article: Hypotenuse, opposite, and adjacent
- Khan video: Intro to the trigonometric ratios
- Khan article: Trigonometric ratios in right triangles

- Khan article: Reciprocal trig ratios
- Khan video: Finding reciprocal trig ratios
- Khan article: Trigonometric ratios review

- Practice Problems:
- Khan Exercise: Trigonometric ratios in right triangles
- Khan Exercise: Reciprocal Trig Functions
- Quizlet Flashcards: Trig Ratios

**3) Trig Ratios with Pythagorean Theorem**

- Explanation:
- Notes | Annotated
- Khan video: Trigonometric ratios in right triangles
- Khan video: Using reciprocal trig ratios

- Practice:
- Worksheet #1
- Worksheet #2

**4) Inverse Trig Ratios**

- Explanation:
- Notes | Annotated Notes
- Khan article: Intro to inverse trig functions

- Practice Problems:
- Khan exercise: Solve for an angle in right triangles
- Worksheet

**5) Solve for missing sides & angles in a right triangle**

- Explanation:
- Practice Problems:
- Khan exercise: Solve for a side in right triangles
- Worksheet #1 | Answers

- Worksheet #2
- Worksheet #3

**6) Relationship of sides and angles in a right triangle**

- Explanation:
- Khan article: Sine & cosine of complementary angles
- Khan video: Sine & cosine of complementary angles
- Khan video: Using complementary angles

- Practice Problems:

**7) Indirect Measurements in a right triangle**

- Explanation:
- Angle of Elevation and Depression: Notes | Annotated
- Khan video: Right triangle word problem
- Khan article: Angles of elevation and depression
- Khan article: Right triangle trigonometry review

- Website - "10 most dangerous landing strips in the world"
- Practice Problems:
- Khan Exercise: Right triangle word problems
- Angle of Elevation and Depression: Worksheet #1 | Answers
- Angle of Elevation and Depression: Worksheet #2 | Answers

**8) Indirect Measurement with unknowns sides**

- Explanation
- Notes | Annotated
- Practice Problems
- Worksheet #2

**9) Law of Sines (for triangles that are not right)**

- Explanation:
- Given two angles and a side: Notes | Annotated
- Given two sides and a non-included angle (non-ambiguous case): Notes | Annotated
- Honors: Given two sides and a non-included angle (ambiguous case): Notes | Annotated
- Khan video: Solving for a side with the law of sines
- Khan video: Solving for an angle with the law of sines
- Khan video: Proof of the law of sines

- Practice Problems
- Khan exercise: Solve triangles using the law of sines
- Worksheet #1 | Answers
- Worksheet #2 | Answers

**10) Law of Cosines (for triangles that are not right)**

- Explanation:
- Notes | Annotated
- Khan video: Solving for a side with the law of cosines
- Khan video: Solving for an angle with the law of cosines
- Khan video: Proof of the law of cosines

- Practice Problems

**11) Review using trig with triangles**

- Explanation
- Notes| Answers
- Khan video: Trig word problem: stars
- Khan article: Laws of sines and cosines review

- Practice Problems:

**12) Navigation**

- Explanation
- Notes | Annotated Notes
- How to use a compass:
- video from REI
- Instructions

- Practice Problems

**13a) Vectors - Basics**

- Explanation:
- Vectors: Notes | Annotated | Animation
- Website: Relative Velocity and Riverboat Problems

- The Physics Classroom
- Khan video: Equivalent vectors
- Khan video: Components of vectors
- Khan video: Components of vectors (example 2)
- Khan video: Vector magnitude from graph
- Khan video: Vector magnitude from components
- Khan video: Vector magnitude from initial & terminal points
- Khan video: Scalar multiplication of vectors
- Khan video: Adding & subtracting vectors
- Khan video: Combined vector operations
- Practice Problems:
- Khan Exercise: Equivalent vectors
- Khan Exercise: Components of vectors
- Khan Exercise: Magnitude of vectors
- Khan Exercise: Scalar multiplication
- Khan Exercise: Add & subtract vectors
- Khan Exercise: Combined vector operations

- Worksheet #1
- Worksheet #2 | Answers
- Interactive game: Vector Investigation â€“ Boat to Island

- Vector addition interactive game

**13b) Vectors: format conversion and addition/subtraction:**

- Explanation:
- Vectors: Notes | Annotated
- Khan video: Unit vectors intro
- Khan video: Direction of vectors from components: 1st & 2nd quadrants
- Khan video: Direction of vectors from components: 3rd & 4th quadrants
- Khan article: Vector forms review
- Khan video: Vector components from magnitude & direction
- Khan article: Vector components from magnitude & direction (advanced)
- Khan article: Vector magnitude and direction review
- Khan video: Vectors word problem: pushing a box
- Khan video: Vectors word problem: hiking

- Practice Problems:
- Khan exercise: Direction of vectors
- Khan exercise: Vector components from magnitude & direction
- Khan exercise: Add vectors: magnitude & direction to component
- Khan exercise: Add vectors: magnitude & direction
- Khan exercise: Vector word problems
- Worksheet #1 | Answers
- Worksheet #2 | Answers

**14) Trig and Area**

- Explanation
- Notes | Annotated
- website with video

- Practice Problems

**15) Review**

__Common Core Standard__: Geometry: Similarity, Right Triangles, and Trig

**Define trigonometric ratios and solve problems involving right triangles:**

- C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- C.7: Explain and use the relationship between the sine and cosine of complementary angles.
- C. 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

**Define trigonometric ratios and solve problems involving right triangles:**

- D.9: Derive the formula
*A*= 1/2*ab*sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. - D.10: Prove the Laws of Sines and Cosines and use them to solve problems.
- D.11: 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).