Find part “a”
Find part “b”

a = 3.74

b = 11.26

Step-by-step explanation:

well to start we have to know the relationships between angles, legs and the hypotenuse.

a: adjacent

o: opposite

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

α = 60°

β = 30°

h = 15

cos α = a/h                   cos β = a/h

cos 60 = x / 15           cos 30 = x / 15

0.5 * 15 = x                 0.866 * 15 = x

x = 7.5                         z = 13

we already calculate all the data of the largest triangle, now we have to calculate y, for this we will calculate it with one of the triangles that is formed with y

sin β = o/h

sin 30 = y / z

0.5 = y / 13

0.5 * 13 = y

y = 6.5

we can apply Pythagoras

h^2 = c1^2 + c2^2

z^2 = y^2 + b^2

13^2 = 6.5^2 + b^2

169 = 42.25 + b^2

169 - 42.25 = b^2

√126.75 = b

b = 11.26

a = 15 - b

a = 15 - 11.26

a = 3.74