Answer:
a =
b = 12
c =
Step-by-step explanation:
Since the triangles are right triangles with 60 and 45 degree angles, their side lengths follow special triangles.
A 45-45-90 right triangle has side lengths .
A 30-60-90 right triangle has side lengths .
Starting with the top triangle which has a 60 degree angle, its side length 6 corresponds to a side length of 1 in the special triangle. It is 6 times bigger so its remaining sides will be 6 times bigger too.
Side a corresponds to side length . Therefore,
.
Side b corresponds to side length 2, b = 2*6 = 12.
The bottom triangle has a 45 degree angle, its side length b= 12 corresponds to . This means
was multiplied by
. This means that side c is
.