The problem that A ship sails for 95.5 miles on a bearing of S 55.3° W. How far west and how far south has the boat traveled? west x mi south x mi Need Help? Read It
The problem that A ship sails for 95.5 miles on a bearing of S 55.3° W. How far west and how far south has the boat traveled? west x mi south x mi Need Help? Read It
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.2: The Law Of Cosines
Problem 3E
Related questions
Question
Section 3.5 Question 16
![**Problem Review: Section 2.5**
**Question:** A ship sails for 95.5 miles on a bearing of S 55.3° W. How far west and how far south has the boat traveled?
**Input Fields:**
- West: [ ] mi ❌
- South: [ ] mi ❌
**Additional Features:**
- Button: [Read It] for additional help.
- Button: [Submit Answer] to check the answer.
**Navigation and Tools:**
- [MY NOTES]
- [ASK YOUR TEACHER]
- [PRACTICE]
In this problem, you will need to use trigonometric functions to break down the distance traveled by the ship into its westward and southward components. Specifically, you use the bearing to create a right triangle and then apply sine and cosine functions to find these components.
Given:
- Distance traveled: \( 95.5 \) miles
- Bearing: \( S 55.3° W \)
To calculate the westward (X) and southward (Y) components:
1. \( X = 95.5 \cos(55.3°) \)
2. \( Y = 95.5 \sin(55.3°) \)
Ensure that your calculator is in degree mode when performing these calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29eaf221-c72e-4b9c-a681-25e14c4a1cc7%2Fcfa42258-27e1-46b8-b26b-b60143a14a04%2Fw5p3on_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Review: Section 2.5**
**Question:** A ship sails for 95.5 miles on a bearing of S 55.3° W. How far west and how far south has the boat traveled?
**Input Fields:**
- West: [ ] mi ❌
- South: [ ] mi ❌
**Additional Features:**
- Button: [Read It] for additional help.
- Button: [Submit Answer] to check the answer.
**Navigation and Tools:**
- [MY NOTES]
- [ASK YOUR TEACHER]
- [PRACTICE]
In this problem, you will need to use trigonometric functions to break down the distance traveled by the ship into its westward and southward components. Specifically, you use the bearing to create a right triangle and then apply sine and cosine functions to find these components.
Given:
- Distance traveled: \( 95.5 \) miles
- Bearing: \( S 55.3° W \)
To calculate the westward (X) and southward (Y) components:
1. \( X = 95.5 \cos(55.3°) \)
2. \( Y = 95.5 \sin(55.3°) \)
Ensure that your calculator is in degree mode when performing these calculations.
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