Sam runs 3.0 miles East, turns left and runs 3.0 miles North and turns right and runs 2.0 miles East. What is the total distance he runs? What is his net displacement? (magnitude in miles and direction as an angle from East towards North.

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Sam runs 3.0 miles East, turns left and runs 3.0 miles North and turns right and runs 2.0 miles East. What is the total distance he runs? What is his net displacement? (magnitude in miles and direction as an angle from East towards North.

Physics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I believe total distance is 8.0 miles but I am having problems with the net displacement which includes the magnitude and direction.
\[d = \sqrt{N^2 + E^2} = \sqrt{(3^2) + (3+2)^2}\]
The angle can be found as follows:\[\tan(\theta) = \left ( N \over E \right ) = \left( 3 \over 5 \right)\]

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