Starting from a crossing that is taken as the origin, a cyclist rides 15 km due east and then 8 km due north.
How far is she from the crossing in a straight line?

She finishes at the point (15, 8). Distance from the origin $=\sqrt{15^2+8^2}=\sqrt{225+64}=\sqrt{289}=17$ km. The 23 km option adds the two legs, which is the distance ridden, not the straight-line distance; $\sqrt{161}$ comes from subtracting the squares (225 - 64) instead of adding them.