What are two different ways you could find the value of a? explain these methods.

See the attached figure to better understand the problem

we know that

1) First way to find the value of a
in the triangle ABC
applying the Pythagorean theorem
AC²=AB²+BC²--------> BC²=AC²-AB²-----> BC²=25²-15²-----> BC²=625-225
BC²=400--------> BC=20 units
a=BC
a=20 units

2) Second way to find the value of a

in the triangle ABD

AB²=AD²+BD²--------> BD²=AB²-AD²-----> BD²=15²-9²---> BD²=144
BD=12 units

in the triangle BDC
a=BC
BC²=BD²+DC²-----> 12²+16²----> 144+256------> BC²=400
BC=20 units
a=20 units

╔═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╗✧   ok, now this, is epic.╚═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╝