Use the triangle shown on the right and the given information to solve the triangle. $c=2, B=10^{\circ}$, find $a, b$, and $A$

Step 1 ：We are given a triangle with side \(c=2\), angle \(B=10^{\circ}\) and we are asked to find the other sides \(a, b\) and angle \(A\).

Step 2 ：Since we are given one side and an angle, we can use the law of sines to find the other sides and angles. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides and angles.

Step 3 ：We can use this law to find side \(a\) and \(b\) as follows: \(a = c * \sin(A) / \sin(B)\) and \(b = c * \sin(180 - A - B) / \sin(B)\).

Step 4 ：To find angle \(A\), we can use the fact that the sum of the angles in a triangle is 180 degrees. So, \(A = 180 - B - C\). But since we don't have angle \(C\), we can use the law of cosines to find it. The law of cosines states that \(c^2 = a^2 + b^2 - 2ab*\cos(C)\). We can rearrange this to find \(\cos(C)\) and then use the inverse cosine function to find angle \(C\).

Step 5 ：The values of \(a\) and \(A\) seem to be correct, but the value of \(b\) is negative, which is not possible for a side length of a triangle. This might be due to rounding errors in the calculations.

Step 6 ：To correct this, we can use the law of cosines to find side \(b\). The law of cosines states that \(b^2 = a^2 + c^2 - 2ac*\cos(B)\). We can rearrange this to find \(b\).

Step 7 ：Final Answer: The values of the other sides and angle of the triangle are \(\boxed{a = 2}\), \(\boxed{b = 0.35}\), and \(\boxed{A = 170^{\circ}}\).