Problem

In $\triangle \mathrm{NOP}, p=490$ inches, $m \angle \mathrm{N}=57^{\circ}$ and $m \angle \mathrm{O}=55^{\circ}$. Find the length of $n$, to the nearest inch.

Answer

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Answer

\(\boxed{443}\)

Steps

Step 1 ：Find angle P: \(180 - 57 - 55 = 68^\circ\)

Step 2 ：Use Law of Sines to find side n: \(\frac{n}{\sin{57^\circ}} = \frac{490 - n}{\sin{55^\circ}}\)

Step 3 ：Solve for n: \(n \approx 443\)

Step 4 ：\(\boxed{443}\)

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