Question

New York and Los Angeles are 2450 mi apart. Find the angle that the arc between these two cities subtends at the center of the earth. (The radius of the earth is 3960 mi.)

Answer 1

To find the angle that the arc between New York and Los Angeles subtends at the center of the earth, we can use the concept of similar triangles. The distance between the two cities is 2450 miles, and the radius of the earth is 3960 miles. By setting up a proportion and solving for the angle, we find that the arc subtends an angle of approximately 44.19° at the center of the earth.

Step-by-step explanation:

To find the angle that the arc between New York and Los Angeles subtends at the center of the earth, we can use the concept of similar triangles. The distance between the two cities is 2450 miles, and the radius of the earth is 3960 miles. We can use the formula for the circumference of a circle to find the circumference of the earth, which is 2π times the radius. Then, by setting up a proportion between the distance between the cities and the circumference of the earth, we can solve for the angle.

Let x be the angle that the arc between the cities subtends at the center of the earth. We can set up the following proportion:

2450 / (2π * 3960) = x / 360°

Solving for x, we get:

x = (2450 * 360°) / (2π * 3960)

Using a calculator to evaluate the expression, we find that the angle is approximately 44.19°. Therefore, the arc between New York and Los Angeles subtends an angle of approximately 44.19° at the center of the earth.