## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 1 - Trigonometric Functions - Section 1.2 Angle Relationships and Similar Triangles - 1.2 Exercises - Page 19: 70a

#### Answer

5,438,000 miles is the maximum distance that Triton can be from Neptune and still cause a total eclipse.

#### Work Step by Step

Let $D_N$ be the sun's distance from Neptune and let $D_S$ be the sun's diameter. Let $d_N$ be Triton's distance from Neptune and let $d_T$ be Triton's diameter. Using similar triangles, we can find the maximum distance that Triton can be from Neptune and still cause a total eclipse: $\frac{D_S}{D_N} = \frac{d_T}{d_N}$ $d_N = \frac{d_T~D_N}{D_S}$ $d_N = \frac{(1680~mi)(2,800,000,000~mi)}{(865,000~mi)}$ $d_N = 5,438,000~mi$ 5,438,000 miles is the maximum distance that Triton can be from Neptune and still cause a total eclipse.

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