Question

apply

1. analyze and persevere it took ines 2 hours to bicycle the perimeter shown at a constant speed of 10 miles per hour. which two roads form the largest angle?

map image with roads: robin rd., king ln., fisher rd., distances 5 mi, 7 mi

Explanation:

Step1: Calculate the perimeter

Use the formula \(d = vt\) (distance = speed × time). Given \(v = 10\) miles per hour and \(t=2\) hours, then \(d=10\times2 = 20\) miles.

Step2: Find the length of Robin Rd.

Let the length of Robin Rd. be \(x\). The perimeter of the triangle (assuming the three - side figure formed by the roads) is \(x + 5+7\). Since the perimeter \(P = 20\), we have \(x+5 + 7=20\). Solving for \(x\): \(x=20-(5 + 7)=8\) miles.

Step3: Apply the Law of Cosines (alternative: use the property that in a triangle, the largest angle is opposite the longest side)

In a triangle, the largest angle is opposite the longest side. The sides of the triangle (formed by the roads) are \(a = 5\), \(b = 7\), \(c = 8\). The longest side is \(c = 8\) (Robin Rd.). The angle opposite to the side of length \(8\) (Robin Rd.) is between King Ln. and Fisher Rd.

Answer:

King Ln. and Fisher Rd.