Answer
$17.1m$
Work Step by Step
Let the distance of the island from the shore be d.
So,
$(\frac{d}{tan30^{\circ}}+\frac{d}{tan40^{\circ}})=50 m $
$\frac{d}{0.577}+\frac{d}{0.84}=50m$
$1.733d+1.19d=50m$
$2.923d=50m$
$d=17.1m$
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