Answer:
a = 3.74
b = 11.26
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