part $1$ of $2$

A river flows at a speed $v_r=4\mathrm{.}88k\frac{m}{h}r$ with respect to the shoreline. A boat needs to go perpendicular to the shoreline to reach a pier on the river's other side. To do so$,$ the boat heads upstream at an angle $=37$ from the direction to the boat's pier.

Find the ratio of $v_b$ to $v_r,$ where $v_r$ is defined above and $v_b$ is the boat's speed with respect to the water.

part $2$ of $2$

If the time taken for the boat to cross the river is $17\mathrm{.}4$min, determine the width of the river.

Answer in units of km$.$ Answer in units of $km.$

$\frac{v_b}{v_r}=\frac{1}{cos}$

$\frac{v_b}{v_r}=tan$

$\frac{v_b}{v_r}=cos$

$\frac{v_b}{v_r}=\frac{1}{si{n}^2}$

$5\frac{v_b}{v_r}=\frac{1}{co{s}^2}$

$\frac{v_b}{v_r}=co{s}^2$

$\frac{v_b}{v_r}=sin$

$\frac{v_b}{v_r}=\frac{1}{sin}$

$9\frac{v_b}{v_r}=si{n}^2$

$\frac{v_b}{v_r}=\frac{1}{tan}$

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