Answer:
804.35+915.26=1719.61
dm
804.35+915.26=1719.61dm.
Step-by-step explanation:
I'll guide you through the solution:
1. **Define Variables:**
Let \( d \) be the distance between the two ships.
2. **Set up Equations:**
\[
\begin{align*}
\tan(47^\circ) &= \frac{1000}{\frac{d}{2}} \\
\tan(32^\circ) &= \frac{1000}{\frac{d}{2}}
\end{align*}
\]
3. **Solve for \( d \):**
\[
\begin{align*}
\frac{1000}{\tan(47^\circ)} &= \frac{d}{2} \\
\frac{1000}{\tan(32^\circ)} &= \frac{d}{2}
\end{align*}
\]
4. **Find \( d \):**
Solve for \( d \) in both equations. I'll provide the numerical values:
\[
\begin{align*}
\frac{1000}{\tan(47^\circ)} &\approx 804.35 \, \text{dm} \\
\frac{1000}{\tan(32^\circ)} &\approx 915.26 \, \text{dm}
\end{align*}
\]
5. **Final Answer:**
The distance between the two ships is approximately \(804.35 + 915.26 = 1719.61 \, \text{dm}\).
