Answer: Therefore, the angle between the kayakers is approximately 63 degrees. The closest answer choice is 78°.
Explanation:
To find the angle between the kayakers, we can use the dot product formula:
F sub 1 · F sub 2 = ||F sub 1|| ||F sub 2|| cos θ
where · denotes the dot product, || || denotes the magnitude, and θ is the angle between the two vectors.
First, we need to find the magnitudes of F sub 1 and F sub 2:
||F sub 1|| = sqrt(190^2 + 160^2) = 247.79
||F sub 2|| = sqrt(128^2 + (-121)^2) = 170.10
Next, we need to find the dot product of F sub 1 and F sub 2:
F sub 1 · F sub 2 = (190)(128) + (160)(-121) = -12080
Substituting these values into the dot product formula, we get:
-12080 = (247.79)(170.10) cos θ
Solving for cos θ, we get:
cos θ = -0.424
Taking the inverse cosine of both sides, we get:
θ ≈ 116.8°
However, this is the angle between the two vectors in standard position (i.e., with initial points at the origin). To find the angle between the kayakers, we need to subtract this angle from 180°:
180° - θ ≈ 63.2°