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Explanation
Step 1
Free body diagram
so, we have a rigth triangle, we can use the Pythagorean theorem to find the hypotensue.
the theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle),so
[tex]\begin{gathered} a^2+b^2=c^2 \\ where\text{ c is the hypotenuse of the right triangle} \end{gathered}[/tex]so
Let
[tex]\begin{gathered} a=\text{ 7 m} \\ b=\text{ 4 m} \\ c=distance\text{ from physicsroom to math classroom} \end{gathered}[/tex]now, replace and solve for c
[tex]\begin{gathered} a^{2}+b^{2}=c^{2} \\ (7m)^2+(4m)^2=c^2 \\ (49)m^2+16(m^2)=c^2 \\ 65=c^2 \\ c=\sqrt{65\text{ }}\text{ meters} \end{gathered}[/tex]therefore, the answer is
[tex]\sqrt{65}[/tex]I hope this helps you
