# Chapter 1 - Trigonometric Functions - Section 1.2 Angle Relationships and Similar Triangles - 1.2 Exercises - Page 19: 69a

236,000 miles is the maximum distance that the moon can be from Earth and still cause a total eclipse.

#### Work Step by Step

Let $D_E$ be the sun's distance from Earth and let $D_S$ be the sun's diameter. Let $d_E$ be the moon's distance from Earth and let $d_M$ be the moon's diameter. Using similar triangles, we can find the maximum distance $d_E$ that the moon can be from Earth and still cause a total eclipse: $\frac{D_S}{D_E} = \frac{d_M}{d_E}$ $d_E = \frac{d_M~D_E}{D_S}$ $d_E = \frac{(2159~mi)(94,500,000~mi)}{(865,000~mi)}$ $d_E = 236,000~mi$ 236,000 miles is the maximum distance that the moon can be from Earth and still cause a total eclipse.

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