Question

Sun's rays at noon 496 mi An estimate of the distance around the earth was done by a scientist who noted that the noontime position of the sun differed by 7°12' from one city to the next closest city. (See the figure.) The distance between these two cities is 496 mi. Use the arc length formula to estimate the radius of Earth. Then find the circumference of Earth. 7° 12 Shadow City A City B 7° 12 The radius of the Earth is approximately mi. (Do not round until the final answer. Then round to the nearest mile as needed.) mi. Therefore, the circumference of the Earth is approximately (Round to the nearest mile as needed.)

Answer 1

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Arce length formula is s=ro where s = arc lengh r = radius o = central angle Here s = 496 mi a = 7° 12' = 7+ 12 60 7.2° 7.2 x 1 180 So, S = TO S 496 X 180 7.28 T r = 3945. 45 45 45 45 45 The radius of the earth is approximately 3945.45 mi - circumference of the earth = 2 Tr = 2 x HX 3945.454545 = 24799. gg circumference of the Earth is approximately 24800 mi