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Andy is attending a school orchestra concert. He sees his math teacher seated $16\,\text{meters}$ ahead of him and his science teacher seated $12\,\text{meters}$ to his right. How far apart are the two teachers? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

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Q. Andy is attending a school orchestra concert. He sees his math teacher seated

16\,\text{meters}

ahead of him and his science teacher seated

12\,\text{meters}

to his right. How far apart are the two teachers?

\newline

\_\_\_\_\_

meters

Identify Positions and Relationship: Identify the positions of the teachers relative to Andy and the relationship between these positions. $\newline$ Andy's math teacher is $16$ meters ahead (straight line), and his science teacher is $12$ meters to the right. This forms a right triangle with Andy at the vertex where the two paths to his teachers meet.
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the distance between the two teachers. $\newline$ Using the formula $a^2 + b^2 = c^2$ , where $a = 16$ meters and $b = 12$ meters. $\newline$ Calculation: $16^2 + 12^2 = c^2$
Calculate Squares: Calculate the squares of $16$ and $12$ . $\newline$ $16^2 = 256$ $\newline$ $12^2 = 144$ $\newline$ Add these to find $c^2$ : $256 + 144 = 400$
Find Distance: Find the square root of $400$ to get the distance $c$ . $\newline$ Calculation: $c = \sqrt{400} = 20$ meters.

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