Question

Mark rides his bike from his house to the closest edge of the park, across the length of the park, and then back home. The distance from his house to the closest edge of the park is 0.9 km and the distance from the far side of the park to his house is 1.6 km. The map shows the path Mark took on his bike. If ∠B = 85° on the map, then use the law of cosines to determine the length of the park in kilometers.

Answer 1

The length of the park is approximately 1.77 kilometers

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.