If they run 3 miles west then 8 miles north, it forms a right triangle. So just use the Pythagorean Theorum.
A^2+B^=C^2
3^2+8^3=C^2
9+64=C^2
Square root 73=C or 8.54=C (Miles)
The runner is 8.54 miles from her starting point if she plans to run straight back.
From the question, a runner jogs 3 miles west and then jogs 8 miles north.
An illustrative diagram for the journey is shown in the attachment below.
In the diagram, S is the starting point. That is, the runner jogs 3 miles west to a place R and then 8 miles north to a place E.
The cardinal points (North, East, West and South) are indicated beside the diagram.
Now, to calculate how far she is from her starting point if she plans to run straight back, we will determine the length of /ES/ in the diagram.
The diagram is a right-angled triangle and /ES/ can be determined using the Pythagorean theorem.
The Pythagorean theorem states that, in a right-angled triangle, the square of the longest side ( that is hypotenuse) equals sum of the squares of the other two sides.
In the diagram, hypotenuse = /ES/
∴ /ES/² = /SR/² + /RE/²
/SR/ = 3 miles
/RE/ =8 miles
/ES/² = 3² + 8²
/ES/² = 9 + 64
/ES/² = 73
/ES/ = [tex]\sqrt{73}[/tex]
/ES/ = 8.54 miles
Hence, the runner is 8.54 miles from her starting point if she plans to run straight back.
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