Given:
DIstance between Diego and Sofia = 3 feet
Distance between Trisha and Diego = 9 feet
Let's find the distance between Sofia and Trisha.
If Sofia is straight behind Diego and directly to the left of Trisha, the figure below represents this situation:
We can see the figure forms a right triangle.
To find the distance between Sofia and Trisha, apply Pytrhagorean Theorem:
[tex]c^2=a^2+b^2[/tex]
Where:
c is the hypotenuse = 9 feet
a is the shorter leg = 3 feet
b is the longer leg = x feet.
Let's solve for b.
We have:
[tex]\begin{gathered} 9^2=3^2+b^2 \\ \\ 81=9+b^2 \\ \\ b^2=81-9 \\ \\ b^2=72 \end{gathered}[/tex]
Take the square root of both sides:
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