QQuestionMathematics
QuestionMathematics
Seattle, Washington (47.4°N, 122.2°W), and San Francisco, California (37.4°N, 122.3°W), have approximately the same longitude, which means that they are roughly due north-south of each other. Use the difference in latitude to approximate the distance between the cities. Assume that the Earth is approximately spherical with a radius of 3960 miles. Round intermediate calculations to 5 decimal places and round your answer to the nearest mile.
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:Let's solve this step by step:
Step 2:: Identify the latitude coordinates
- Seattle: $$47.4°N
- San Francisco: 37.4°N
Step 3:: Calculate the latitude difference
\Delta \text{latitude} = 47.4° - 37.4° = 10°
Step 4:: Convert degrees to radians
- We'll use the conversion: $$1° = \frac{\pi}{180} \text{ radians}
\Delta \text{latitude in radians} = 10° \times \frac{\pi}{180} = \frac{10\pi}{180} = 0.17453 \text{ radians}
Step 5:: Calculate arc length using great circle distance formula
\text{Distance} = 3960 \times 0.17453 = 691.34 \text{ miles}
- Earth's radius = 3960 miles
Final Answer
The approximate distance between Seattle and San Francisco is 691 miles.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students