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.

Explanation:

Step1: Identify the right triangle

The two paths form a right triangle, where the straight path (1190 feet) is the hypotenuse, the northward walk (660 feet) is one leg, and the westward walk (let's call it \( x \)) is the other leg.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \( a \), \( b \) and hypotenuse \( c \), \( a^{2}+b^{2}=c^{2} \). Here, \( a = 660 \), \( c = 1190 \), and we need to find \( b=x \). So we have the equation \( 660^{2}+x^{2}=1190^{2} \).

Step3: Solve for \( x \)

First, calculate \( 660^{2}=435600 \) and \( 1190^{2} = 1416100 \). Then, rewrite the equation as \( x^{2}=1190^{2}-660^{2}=1416100 - 435600=980500 \). Now, take the square root of both sides: \( x=\sqrt{980500}\approx990.2 \). Rounding to the nearest whole number, \( x\approx990 \).

Answer:

990