Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Let's break this down step-by-step to find how far the airplane is from the starting point (point A).
1. Understanding the Problem:
- The airplane flies 120 miles from point A at an angle of 110°.
- Then, it changes direction and flies 70 miles at an angle of 255°.
- We need to compute the distance from the final position back to the starting point A.
2. Breaking Down into Components:
We will split the movement into horizontal (x) and vertical (y) components based on trigonometry principles:
- Distance 1: 120 miles at 110°
- [tex]\( x_1 = 120 \cos(110°) \)[/tex]
- [tex]\( y_1 = 120 \sin(110°) \)[/tex]
- Distance 2: 70 miles at 255°
- [tex]\( x_2 = 70 \cos(255°) \)[/tex]
- [tex]\( y_2 = 70 \sin(255°) \)[/tex]
3. Calculating Total Displacement Components:
Summing the individual components to get the total displacement:
- Total horizontal displacement, [tex]\( x_{total} = x_1 + x_2 \)[/tex]
- Total vertical displacement, [tex]\( y_{total} = y_1 + y_2 \)[/tex]
4. Resulting Components:
The x and y components after each segment of the trip are:
- [tex]\( x_{total} \approx -59.16 \)[/tex]
- [tex]\( y_{total} \approx 45.15 \)[/tex]
5. Computing the Overall Distance:
The straight-line distance (displacement) back to point A can be calculated using the Pythagorean theorem:
[tex]\[ D = \sqrt{x_{total}^2 + y_{total}^2} \][/tex]
Substituting the values:
[tex]\[ D = \sqrt{(-59.16)^2 + (45.15)^2} \][/tex]
6. Final Calculation:
- The calculated distance is approximately: [tex]\( D \approx 74 \)[/tex] miles.
Thus, the airplane is approximately 74 miles from point A.
1. Understanding the Problem:
- The airplane flies 120 miles from point A at an angle of 110°.
- Then, it changes direction and flies 70 miles at an angle of 255°.
- We need to compute the distance from the final position back to the starting point A.
2. Breaking Down into Components:
We will split the movement into horizontal (x) and vertical (y) components based on trigonometry principles:
- Distance 1: 120 miles at 110°
- [tex]\( x_1 = 120 \cos(110°) \)[/tex]
- [tex]\( y_1 = 120 \sin(110°) \)[/tex]
- Distance 2: 70 miles at 255°
- [tex]\( x_2 = 70 \cos(255°) \)[/tex]
- [tex]\( y_2 = 70 \sin(255°) \)[/tex]
3. Calculating Total Displacement Components:
Summing the individual components to get the total displacement:
- Total horizontal displacement, [tex]\( x_{total} = x_1 + x_2 \)[/tex]
- Total vertical displacement, [tex]\( y_{total} = y_1 + y_2 \)[/tex]
4. Resulting Components:
The x and y components after each segment of the trip are:
- [tex]\( x_{total} \approx -59.16 \)[/tex]
- [tex]\( y_{total} \approx 45.15 \)[/tex]
5. Computing the Overall Distance:
The straight-line distance (displacement) back to point A can be calculated using the Pythagorean theorem:
[tex]\[ D = \sqrt{x_{total}^2 + y_{total}^2} \][/tex]
Substituting the values:
[tex]\[ D = \sqrt{(-59.16)^2 + (45.15)^2} \][/tex]
6. Final Calculation:
- The calculated distance is approximately: [tex]\( D \approx 74 \)[/tex] miles.
Thus, the airplane is approximately 74 miles from point A.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.