Use a calculator, spreadsheet, or another tool to solve for the unknown sides of the given right triangle. The length of the hypotenuse is $10 . a$ is the length of the side opposite the $10^{\circ}$ angle and $b$ is the length of the side opposite angle $B$.
Round your answers to four decimal places.
\[
\begin{array}{l}
a \approx \text { Number } \\
b \approx \text { Number }
\end{array}
\]

Step 1 ：We are given a right triangle with a hypotenuse of length 10 units, and one of the angles is 10 degrees. We are asked to find the lengths of the other two sides, denoted as 'a' and 'b'.

Step 2 ：We can use the sine rule to find the length of side 'a'. The sine rule states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Therefore, we can express 'a' as: \(a = 10 \times \sin(10^\circ)\)

Step 3 ：Calculating the above expression, we find that \(a \approx 1.7365\)

Step 4 ：We can then use the Pythagorean theorem to find the length of side 'b'. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, we can express 'b' as: \(b = \sqrt{10^2 - a^2}\)

Step 5 ：Substituting the value of 'a' into the above expression, we find that \(b \approx 9.8481\)

Step 6 ：Final Answer: The length of side 'a' is approximately \(\boxed{1.7365}\) and the length of side 'b' is approximately \(\boxed{9.8481}\)