elias and jerry have two options to walk from their school to a corner store. • option 1: walk 660 feet due…

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.

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.

Answer

Explanation:

Step1: Identify the problem as a right - triangle problem

The two - part walk in option 1 forms the two legs of a right - triangle, and the straight - path in option 2 is the hypotenuse. Let the north - ward distance be $a = 660$ feet, the west - ward distance be $b$, and the hypotenuse $c=1190$ feet. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $b$

We can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values of $a$ and $c$

Substitute $a = 660$ and $c = 1190$ into the formula: $b=\sqrt{1190^{2}-660^{2}}=\sqrt{(1190 + 660)(1190 - 660)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $(1190 + 660)=1850$ and $(1190 - 660)=530$. Then $b=\sqrt{1850\times530}=\sqrt{980500}$.

Step4: Calculate the value of $b$

$b=\sqrt{980500}\approx990.2$.

Step5: Round to the nearest whole number

Rounding $990.2$ to the nearest whole number gives $990$.

Answer:

$990$