Three people are sitting on a bus. Eva is seated 6 feet directly behind Mona and 8 feet directly left of Todd. How far is Mona from Todd? _____ feet

Identify Positions: Step 1: Identify the positions of Eva, Mona, and Todd. Eva is 6 feet behind Mona and 8 feet left of Todd. We need to find the distance between Mona and Todd.Visualize as Triangle: Step 2: Visualize the scenario as a right triangle. Mona is at one vertex, Todd at another, and the right angle is at Eva's position. The legs of the triangle are the distances from Eva to Mona and Eva to Todd.Use Pythagorean Theorem: Step 3: Use the Pythagorean Theorem to find the distance between Mona and Todd. The distances form the legs of the triangle, so: $6^2 + 8^2 = x^2$Calculate Squares: Step 4: Calculate the squares of the legs. $6^2 = 36$ $8^2 = 64$ $36 + 64 = x^2$Add to Find x^2: Step 5: Add the squares to find $x^2$. $36 + 64 = 100$ $x^2 = 100$Solve for x: Step 6: Solve for $x$ by taking the square root of $x^2$. $\sqrt{100} = 10$ So, Mona is 10 feet from Todd.

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Three people are sitting on a bus. Eva is seated $6\,\text{feet}$ directly behind Mona and $8\,\text{feet}$ directly left of Todd. How far is Mona from Todd? $\newline$ $\_\_\_\_\_$ feet

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Grade 8

Pythagorean theorem: word problems

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Q. Three people are sitting on a bus. Eva is seated

6\,\text{feet}

directly behind Mona and

8\,\text{feet}

directly left of Todd. How far is Mona from Todd?

\newline

\_\_\_\_\_

feet

Identify Positions: Step $1$ : Identify the positions of Eva, Mona, and Todd. $\newline$ Eva is $6$ feet behind Mona and $8$ feet left of Todd. We need to find the distance between Mona and Todd.
Visualize as Triangle: Step $2$ : Visualize the scenario as a right triangle. $\newline$ Mona is at one vertex, Todd at another, and the right angle is at Eva's position. The legs of the triangle are the distances from Eva to Mona and Eva to Todd.
Use Pythagorean Theorem: Step $3$ : Use the Pythagorean Theorem to find the distance between Mona and Todd. $\newline$ The distances form the legs of the triangle, so: $\newline$ $6^2 + 8^2 = x^2$
Calculate Squares: Step $4$ : Calculate the squares of the legs. $\newline$ $6^2 = 36$ $\newline$ $8^2 = 64$ $\newline$ $36 + 64 = x^2$
Add to Find x^ $2$ : Step $5$ : Add the squares to find $x^2$ . $\newline$ $36 + 64 = 100$ $\newline$ $x^2 = 100$
Solve for x: Step $6$ : Solve for $x$ by taking the square root of $x^2$ . $\newline$ $\sqrt{100} = 10$ $\newline$ So, Mona is $10$ feet from Todd.