Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 1 - Trigonometric Functions - Section 1.2 Angle Relationships and Similar Triangles - 1.2 Exercises: 70a

Answer

1,830,000 miles is the maximum distance that Ganymede can be from Jupiter and still cause a total eclipse.

Work Step by Step

Let $D_J$ be the sun's distance from Jupiter and let $D_S$ be the sun's diameter. Let $d_J$ be Ganymede's distance from Jupiter and let $d_G$ be Ganymede's diameter. Using similar triangles, we can find the maximum distance that Ganymede can be from Jupiter and still cause a total eclipse: $\frac{D_S}{D_J} = \frac{d_G}{d_J}$ $d_J = \frac{d_G~D_J}{D_S}$ $d_J = \frac{(3270~mi)(484,000,000~mi)}{(865,000~mi)}$ $d_J = 1,830,000~mi$ 1,830,000 miles is the maximum distance that Ganymede can be from Jupiter and still cause a total eclipse.
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