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Answer :

The cosine rule is used to determine the values of unknown aides and angles in a triangle

The measure of θ is approximately 117.2°

Reason:

Given parameters are;

The distance between the two windmills, a = 456 feet

The distance between the cow and one of the windmills, b = 320 feet

Distance between the cow and the other windmills, c = 210 feet

Required, the angle θ between b, and c direction

Solution;

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(θ)

  • [tex]cos (\theta) = \dfrac{b^2 + c^2 - a^2}{2 \cdot b \cdot c }[/tex]

Which gives;

[tex]cos (\theta) = \dfrac{320^2 + 210^2 - 456^2}{2 \times 320 \times 210 }[/tex]

  • [tex]\theta = arcos \left(\dfrac{320^2 + 210^2 - 456^2}{2 \times 320 \times 210 }\right) \approx 117.2 ^{\circ}[/tex]

The measure of θ ≈ 117.2°

Learn more about the cosine rule here: