Answer
The speed of the current is 3.5 mph
The actual speed of the motorboat is 19.7 mph
Work Step by Step
Let $v_b$ be the speed of the motorboat in still water.
Let $v_c$ be the speed of the current.
Let $v_m$ be the actual speed of the motorboat. Note that the vector $v_m = v_b+v_c$
These three vectors form a right triangle where $v_b$ is the hypotenuse.
We can find $v_c$:
$\frac{v_c}{v_b} = sin~10^{\circ}$
$v_c = v_b~sin~10^{\circ}$
$v_c = (20.0~mph)~sin~10^{\circ}$
$v_c = 3.5~mph$
The speed of the current is 3.5 mph
We can find $v_m$:
$\frac{v_m}{v_b} = cos~10^{\circ}$
$v_m = v_b~cos~10^{\circ}$
$v_m = (20.0~mph)~cos~10^{\circ}$
$v_m = 19.7~mph$
The actual speed of the motorboat is 19.7 mph
