1. You can make use of the Pythagorean theorem considering "a" to be the longer leg of the largest right triangle. Then the value of "a" can be calculated from
(16+9)² = 15² +a²
625 -225 = a²
√400 = a = 20
2. You can find the altitude of the largest triangle (the length of the unmarked vertical line), then find "a" as the hypotenuse of the medium-sized right triangle.
That altitude is ...
√(15² -9²) = √144 = 12
so the length "a" is ...
a² = 12² +16² = 144 +256 = 400
a = √400 = 20
3. Based on the 15 and 9 dimensions of the smallest right triangle, you can realize that these triangles are multiples of the 3-4-5 right triangle. Then you can use relevant ratios of the side lengths of any of the triangles of which "a" is a part.
a = 4/3×15 = 4/5×(9+16) = 5/4×16 = 20