horses pull a cart. The first horse weighs 1300lbs and the second weights 1610lbs. If the angle between them is 21° Two find the resultant force of the cart. (Round your answer to the nearest whole pound)
horses pull a cart. The first horse weighs 1300lbs and the second weights 1610lbs. If the angle between them is 21° Two find the resultant force of the cart. (Round your answer to the nearest whole pound)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Problem Statement
Two horses pull a cart. The first horse weighs 1300 lbs and the second weighs 1610 lbs. If the angle between them is 21°, find the resultant force on the cart. (Round your answer to the nearest whole pound.)
---
To solve this problem, we will need to use vector addition. The forces exerted by each horse can be considered as vectors, and the resulting force can be found using the Law of Cosines.
The magnitude of the resultant force \( R \) can be found using the following formula:
\[ R = \sqrt{F_1^2 + F_2^2 + 2 \cdot F_1 \cdot F_2 \cdot \cos(\theta)} \]
Where:
- \( F_1 \) is the force exerted by the first horse (1300 lbs)
- \( F_2 \) is the force exerted by the second horse (1610 lbs)
- \( \theta \) is the angle between the two forces (21°)
Now, substituting the given values into the formula:
\[ R = \sqrt{1300^2 + 1610^2 + 2 \cdot 1300 \cdot 1610 \cdot \cos(21°)} \]
### Step-by-Step Solution
1. **Calculate \( 1300^2 \):**
\[ 1300^2 = 1690000 \]
2. **Calculate \( 1610^2 \):**
\[ 1610^2 = 2592100 \]
3. **Calculate \( 2 \cdot 1300 \cdot 1610 \cdot \cos(21°) \):**
First, find \( \cos(21°) \). You will need a calculator for this or use a cosine table.
\[ \cos(21°) \approx 0.933 \]
Then:
\[ 2 \cdot 1300 \cdot 1610 \cdot 0.933 \]
\[ = 2 \cdot 1300 \cdot 1610 \cdot 0.933 \]
\[ = 2 \cdot 2093000 \cdot 0.933 \]
\[ = 3902900 \cdot 0.933 \]
\[ \approx 3638673 \]
4. **Sum the squares and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb77dd63d-90e0-4a84-b222-b885a237b41a%2Fbf0dd881-eb41-4a39-ad43-d3225d92300b%2Fhs4n1v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Two horses pull a cart. The first horse weighs 1300 lbs and the second weighs 1610 lbs. If the angle between them is 21°, find the resultant force on the cart. (Round your answer to the nearest whole pound.)
---
To solve this problem, we will need to use vector addition. The forces exerted by each horse can be considered as vectors, and the resulting force can be found using the Law of Cosines.
The magnitude of the resultant force \( R \) can be found using the following formula:
\[ R = \sqrt{F_1^2 + F_2^2 + 2 \cdot F_1 \cdot F_2 \cdot \cos(\theta)} \]
Where:
- \( F_1 \) is the force exerted by the first horse (1300 lbs)
- \( F_2 \) is the force exerted by the second horse (1610 lbs)
- \( \theta \) is the angle between the two forces (21°)
Now, substituting the given values into the formula:
\[ R = \sqrt{1300^2 + 1610^2 + 2 \cdot 1300 \cdot 1610 \cdot \cos(21°)} \]
### Step-by-Step Solution
1. **Calculate \( 1300^2 \):**
\[ 1300^2 = 1690000 \]
2. **Calculate \( 1610^2 \):**
\[ 1610^2 = 2592100 \]
3. **Calculate \( 2 \cdot 1300 \cdot 1610 \cdot \cos(21°) \):**
First, find \( \cos(21°) \). You will need a calculator for this or use a cosine table.
\[ \cos(21°) \approx 0.933 \]
Then:
\[ 2 \cdot 1300 \cdot 1610 \cdot 0.933 \]
\[ = 2 \cdot 1300 \cdot 1610 \cdot 0.933 \]
\[ = 2 \cdot 2093000 \cdot 0.933 \]
\[ = 3902900 \cdot 0.933 \]
\[ \approx 3638673 \]
4. **Sum the squares and
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