16 Chapter 1 • Right Triangle Trigonometry §1.3 Example 1.15 O A B α As another application of trigonometry to astronomy, we will Fnd the distance from the earth to the sun. Let O be the center of the earth, let A be a point on the equator, and let B represent an object (e.g. a star) in space, as in the picture on the right. If the earth is positioned in such a way that the angle ∠ OAB = 90 ◦ , then we say that the angle α = ∠ OBA is the equatorial parallax of the object. The equatorial parallax of the sun has been observed to be ap-proximately α = 0.00244 ◦ . Use this to estimate the distance from the center of the earth to the sun. Solution: Let B be the position of the sun. We want to Fnd the length of OB . We will use the actual radius of the earth, mentioned at the end of Example 1.14, to get OA = 3956.6 miles. Since ∠ OAB = 90 ◦ , we have OA OB = sin α ⇒ OB = OA sin α = 3956.6 sin 0.00244 ◦ = 92908394 , so the distance from the center of the earth to the sun is approximately 93 million miles
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