Answer:
[tex]d=16.9\ m[/tex]
Step-by-step explanation:
Let
[tex]A(0,0)[/tex] -----> Andrew's initial location
we know that
1) He travels 5 meters 90°north
At this moment Andrew's location is
[tex]B(0,0+5)\\B(0,5)[/tex]
2) He moves 13 meters 45° east
At this moment Andrew's location is
[tex]C(0+13cos(45^o),5+13sin(45^o))[/tex]
[tex]C(0+13\frac{\sqrt{2}}{2},5+13\frac{\sqrt{2}}{2})[/tex]
[tex]C(13\frac{\sqrt{2}}{2},5+13\frac{\sqrt{2}}{2})[/tex]
3) Find the distance between Andrew's initial location to the hidden treasure.
Find the distance between point A and point C
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(0,0)[/tex]
[tex]C(13\frac{\sqrt{2}}{2},5+13\frac{\sqrt{2}}{2})[/tex]
substitute the values
[tex]d=\sqrt{(5+13\frac{\sqrt{2}}{2}-0)^{2}+(13\frac{\sqrt{2}}{2}-0)^{2}}[/tex]
[tex]d=16.9\ m[/tex]
