Answer
$$a\approx54.7$$
Work Step by Step
Use the Pythagorean Theorem:
$$c^{2}=a^{2}+b^{2}.$$
Rearrange terms:
$$a^{2}=c^{2}-b^{2}.$$
Substitute in $b=100$ and $c=114:$
$$a^{2}=114^{2}-100^{2}=12996-10000=2996.$$
Take the square root of both sides and round to the nearest tenth:
$$\sqrt {a^{2}}=\sqrt {2996}$$
$$a\approx54.7.$$
