0.74 mi. 0.86 mi. 2.21 mi 2.35 mi

To solve this problem, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and an angle γ opposite side c, the following equation holds:\[c^2 = a^2 + b^2 - 2ab \cdot \cos(\gamma)\]In this case, we are looking for the distance from the School to the Park, which we will call side c. We know the following:- The distance from School to Joey's House (side a) is 1.2 miles.- The distance from Park to Joey's House (side b) is 1.3 miles.- The angle between School and Joey's House (angle γ) is 40°.We can plug these values into the Law of Cosines to find the length of side c:\[c^2 = a^2 + b^2 - 2ab \cdot \cos(\gamma)\]\[c^2 = (1.2)^2 + (1.3)^2 - 2 \cdot (1.2) \cdot (1.3) \cdot \cos(40°)\]Now, let's calculate it step by step:1. Calculate \(a^2\) and \(b^2\):\[a^2 = (1.2)^2 = 1.44\]\[b^2 = (1.3)^2 = 1.69\]2. Calculate \(2ab \cdot \cos(\gamma)\):First, we need to calculate the cosine of 40°. We will use a calculator for this since the cosine of 40° is not a commonly memorized value.\[\cos(40°) \approx 0.766\]\[2ab \cdot \cos(\gamma) = 2 \cdot 1.2 \cdot 1.3 \cdot 0.766\]\[2ab \cdot \cos(\gamma) \approx 2 \cdot 1.2 \cdot 1.3 \cdot 0.766 \approx 2.39856\]3. Substitute the values into the Law of Cosines equation:\[c^2 = 1.44 + 1.69 - 2.39856\]\[c^2 = 3.13 - 2.39856\]\[c^2 \approx 0.73144\]4. Take the square root to find c:\[c \approx \sqrt{0.73144}\]\[c \approx 0.8555\]The distance from the School to the Park is approximately 0.86 miles.Final Answer: \(0.86 \mathrm{mi}\).