Andy is attending a school orchestra concert. He sees his math teacher seated 16 meters ahead of him and his science teacher seated 12 meters to his right. How far apart are the two teachers? _____ meters

Identify Positions and Relationship: Identify the positions of the teachers relative to Andy and the relationship between these positions. 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. Using the formula $a^2 + b^2 = c^2$, where $a = 16$ meters and $b = 12$ meters. Calculation: $16^2 + 12^2 = c^2$Calculate Squares: Calculate the squares of 16 and 12. $16^2 = 256$ $12^2 = 144$ Add these to find $c^2$: $256 + 144 = 400$Find Distance: Find the square root of 400 to get the distance $c$. Calculation: $c = \sqrt{400} = 20$ meters.

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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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Grade 8

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.