Solve the triangle for the unknown angle θ and side x. Given: side a=10, side b=8, angle A=47°.

Using the sine rule:

Rearrange to solve for $\sin \theta$:

Rounding to four decimal places as in the image:

Take the inverse sine of the value:

Rounding to two decimal places as in the image:

The sum of angles in a triangle is $180^\circ$.
Third angle $= 180^\circ - 47^\circ - 66.09^\circ$
Third angle $= 180^\circ - 113.09^\circ$
Third angle $= 66.91^\circ$

Using the sine rule with the third angle and the known side:

Rearrange to solve for $x$:

Rounding to two decimal places as in the image:

The steps and calculations provided in the image are correct.
The final answer is $\text{10.06 km}$.