After the turn Mario and Lee are going 35^(∘) north of east instead of 35^(∘) east of north.
They are not going in the right direction.
Path of Luther and Stephanie
To find the direction of Luther and Stephanie's path, let's investigate the diagram and find the measure of ∠ θ.
Since the direction to the north is perpendicular to the east-west direction, angle ∠ θ together with a right angle form the given angle that measures 125^(∘).
After the turn Luther and Stephanie are going 35^(∘) east of north.
They are going in the right direction.
b Let's summarize what we know about the two triangles on the diagram.
Claim
Justification
TS≅TM
Both segments represent a walk of 75 feet.
m∠ FTS< m∠ FTM
Angle ∠ FTS is part of angle ∠ FTM.
Since FT is a common side, triangles △ FTS and △ FTM have two pairs of congruent sides.
This means that we can apply the Hinge Theorem.
m∠ FTS< m∠ FTM
⇓
FS< FM
Luther and Stephanie are closest to the fountain when the pairs stop.
