Two ships leave the same port at the same time. two hours later ship a has traveled 12 miles and ship b has traveled 8 miles.

if they are currently 16 miles apart, what is the angle between their paths?

the angle between their paths is 100.8°

Step-by-step explanation:

From the given information, you can construct a triangle, just like the one in the figure.

We will use the Cosine Rule which is:

c² = b² + a² - 2 b c cos(θ)

where

Therefore,

2 b c cos(θ) = b² + a² - c²

cos(θ) = (b² + a² - c²) / 2 b c

θ = cos⁻¹( (b² + a² - c²) / (2 b c) )

θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )

θ = 100.8°

Therefore, the angle between their paths is 100.8°