Answer:
Let AB be the light house and two ships be at C and D. In \[\Delta \text{ }ABC\], \[\frac{BC}{AB}=\cot \,45{}^\circ \] \[\Rightarrow \] \[\frac{x}{100}=1\] \[\Rightarrow \] \[x=100\] ...(i) Similarly, in \[\Delta \text{ }ABD\], \[\frac{BD}{AB}=\cot \,\,30{}^\circ \] \[\Rightarrow \] \[\frac{y}{100}=\sqrt{3}\] \[\Rightarrow \] \[y=100\sqrt{3}\] ?(ii) Distance between two ships \[=y-x\] \[=100\sqrt{3}-100\] [from (i) and (ii)] \[=100\left( \sqrt{3}-1 \right)\] \[=100(1.732-1)\] \[=73.2\,\,m\]
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