Answer
$b\approx5.4, A\approx68^\circ, C\approx22^\circ$
Work Step by Step
Step 1. Based on the given conditions, using the Pythagorean Theorem, we have
$b=\sqrt {a^2+c^2}=\sqrt {5^2+2^2}=\sqrt {29}\approx5.4$
Step 2. For angle $A$, in the right triangle, we have
$tanA=\frac{a}{c}=2.5$, thus $A=tan^{-1}(2.5)\approx68^\circ$
Step 3. We can find the angle as
$C=90^\circ-68^\circ=22^\circ$
Step 4. We solved the triangle with
$b\approx5.4, A\approx68^\circ, C\approx22^\circ$
