Consider a triangle $A B C$ like the one below. Suppose that $B=46^{\circ}, C=106^{\circ}$, and $a=64$. (The figure is not drawn to scale.) Solve the triangle. Espanol Round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or". \[ A=\square \circ b=\square, c= \]

Step 1 ：Given a triangle $A B C$ with $B=46^{\circ}, C=106^{\circ}$, and $a=64$.

Step 2 ：We know that the sum of the angles in a triangle is 180 degrees. So we can calculate angle A by subtracting the given angles B and C from 180. This gives us $A = 180 - B - C = 180 - 46 - 106 = 28^{\circ}$.

Step 3 ：We can use the law of sines to find the lengths of sides b and c. 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 of the triangle.

Step 4 ：So, we can set up the following equations to find b and c: $b = a * \frac{\sin(B)}{\sin(A)}$ and $c = a * \frac{\sin(C)}{\sin(A)}$.

Step 5 ：Substituting the given values into the equations, we get $b = 64 * \frac{\sin(46)}{\sin(28)} \approx 98.1$ and $c = 64 * \frac{\sin(106)}{\sin(28)} \approx 131.0$.

Step 6 ：Final Answer: \(A=\boxed{28^{\circ}}, b=\boxed{98.1}, c=\boxed{131.0}\)