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Sagot :
Answer:
The length of the park is approximately 1.77 kilometers
Step-by-step explanation:
The law of cosines is most appropriate when the measures of two sides and the included angle formed n=by the path of motion is known
The given parameters of the question are;
The distance from Mark's house to the edge of the park, a = 0.9 km
The distance from the far side of the park to Mark's house, c = 1.6 km
Whereby the included angle between lines, 'a' and 'c' is the ∠B = 85°, by cosine rule, we have;
b² = a² + c² - 2·a·c·cos(B)
Where;
b = The length of the park in kilometers
By plugging in the known values of 'a', 'b', and 'c', we get;
b² = 0.9² + 1.6² - 2 × 0.9 × 1.6 × cos(85°) ≈ 3.11899146089
∴ b = √(3.11899146089) ≈ 1.76606666377
Therefore, the length of the park, b ≈ 1.77 km.
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