Prepare to delve into the captivating realm of geometry as we unveil the Unit 8 Right Triangles and Trigonometry Homework 1 Answer Key. This comprehensive guide serves as an invaluable resource, illuminating the intricacies of right triangles and trigonometry with clarity and precision.
Within these pages, you will embark on a journey of discovery, mastering the fundamental concepts of trigonometry and applying them to real-world scenarios. Whether you are a student seeking guidance or an educator seeking to enhance your teaching, this answer key will empower you with the knowledge and confidence to conquer the challenges of geometry.
Unit 8 Right Triangles and Trigonometry Homework 1: Unit 8 Right Triangles And Trigonometry Homework 1 Answer Key
This homework assignment aims to reinforce the fundamental concepts of right triangles and trigonometry, including the Pythagorean theorem, trigonometric ratios, and solving trigonometric equations.
Upon completing this homework, students will be able to:
- Apply the Pythagorean theorem to solve problems involving right triangles.
- Calculate trigonometric ratios (sine, cosine, tangent) using the definitions and properties of right triangles.
- Solve trigonometric equations involving sine, cosine, and tangent.
Answer Key for Unit 8 Right Triangles and Trigonometry Homework 1, Unit 8 right triangles and trigonometry homework 1 answer key
| Question | Answer | Explanation |
|---|---|---|
| 1. Find the length of the hypotenuse of a right triangle with legs of length 3 and 4. | 5 | Use the Pythagorean theorem: a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. So, 32 + 42 = c2, which gives c2 = 25. Therefore, c = √25 = 5. |
| 2. Find the sine of the angle opposite the side of length 3 in the triangle from question 1. | 3/5 | The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the side of length 3, and the hypotenuse is of length 5. So, sin(angle) = 3/5. |
| 3. Find the value of cos(45°) | √2/2 | The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In a 45°-45°-90° triangle, the adjacent side and the hypotenuse are of equal length. So, cos(45°) = √2/2. |
| 4. Solve the equation sin(x) = 0.5 | x = 30° + 180°n, where n is an integer | The sine of an angle is 0.5 when the angle is 30°. To find all solutions, we add multiples of 180° (which represents a full rotation) to 30°. So, the solutions are x = 30° + 180°n, where n is an integer. |
Key Questions Answered
What is the purpose of this homework assignment?
This homework assignment is designed to reinforce your understanding of the concepts covered in Unit 8: Right Triangles and Trigonometry.
What learning objectives are covered in this homework?
This homework covers the following learning objectives:
- Understanding the definitions and properties of right triangles
- Applying trigonometric ratios (sine, cosine, tangent) to solve problems
- Using the Pythagorean theorem to find missing side lengths
How can I use this answer key effectively?
Use this answer key to check your answers and identify areas where you need further review. Refer to the provided explanations and examples to enhance your understanding of the concepts.
