Astronomical measurements are often made by computing the small angle formed by

Question

Astronomical measurements are often made by computing the small angle formed by the extremities of a distant object and using the arc length to approximate the chord. In the picture below, the full moon is shown to form an angle of 1/2 degrees when the distance indicated is 248,000 miles. Estimate the diameter of the moon using this method.

Astronomical measurements are often made by computing the smal angle formed by the extremities of a distant object and using the arc length to approximate the chord. In the picture below, the full moon is shown to form an angle of when the distance indicated is 248,000 miles. Estimate the diameter of the moon using this method. (Round your answer to two decimal places.) 2164x mi 2 moon 248,000 miles earth

Explanation / Answer

Radius and tangent are always perpendicular . SO if we draw a radius of moon that is perpendicular to the tangent , and joining the center of moon to the intersection of the two tangents, we will get a right triangle with adjacent = 248000miles , theta =0.5/2 degree.

Let the radius =r

tan theta = r/248000

r = 248000 tan 0.25 = 1082.11

So diameter = 2 * 1082.11 = 2164.22mi

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