Question

elias and jerry have two options to walk from their school to a corner store. • option 1: walk 660 feet due north and then turn and walk due west • option 2: walk 1,190 feet on a straight path directly to the store through a park how many feet due west will elias and jerry walk if they choose option 1? round your answer to the nearest whole number. type the number in the box.

Explanation:

Step1: Identify the right triangle

The path forms a right triangle, where the straight path (1190 feet) is the hypotenuse, the northward walk (660 feet) is one leg, and the westward walk (\(x\)) is the other leg.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs. Let \(a = 660\), \(c = 1190\), and \(b = x\). So we have \(660^2 + x^2 = 1190^2\).

Step3: Solve for \(x\)

First, calculate \(660^2 = 435600\) and \(1190^2 = 1416100\). Then, rearrange the formula to \(x^2 = 1190^2 - 660^2 = 1416100 - 435600 = 980500\). Take the square root of 980500: \(x = \sqrt{980500} \approx 990.2\). Rounding to the nearest whole number gives \(x \approx 990\).

Answer:

990