c = 22.3 km
Step-by-step explanation:
You can solve this problem using cosine law:
[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos( \gamma ) [/tex]
where a and b are the legs of the triangle, c is the unknown length and the angle gamma is the angle opposite length c. We know that
a = 50 km
b= 52.4 km
gamma = 25°
c^2 = (50 km)^2 + (52.4 km)^2 -2(50)(52.4)cos25°
= 496.707 km^2
or
c = 22.3 km
