Exercise 30 Page 378

Practice makes perfect

a Let's label some points on the map.

$F$ is the fountain.
$T$ is the turning point.
$M$ is the point Mario and Lee reach.
$S$ is the point Luther and Stephanie reach.

Let's examine the two paths separately.

Path of Mario and Lee

After the turn Mario and Lee are going $3 5^{\circ}$ north of east instead of $3 5^{\circ}$ 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

12 5^{\circ} .

m ∠ θ + 90 = 125

SubEqn

$LHS - 90 = RHS - 90$

m ∠ θ = 35

After the turn Luther and Stephanie are going

3 5^{\circ}

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
$\overline{T S} ≅ \overline{T M}$	Both segments represent a walk of $75$ feet.
$m ∠ F T S < m ∠ F T M$	Angle $∠ F T S$ is part of angle $∠ F T M .$

Since

\overline{F T}

is a common side, triangles

△ F T S

and

△ F T M

have two pairs of congruent sides. This means that we can apply the Hinge Theorem.

m ∠ F T S < m ∠ F T M ⇓ F S < F M

Luther and Stephanie are closest to the fountain when the pairs stop.

Subchapter links

Check Your Understanding p.375-376

H.O.T. Problems p.379

Standardized Test Practice p.380

Spiral Review p.380

Skills Review p.380

Exercise 30 Page 378

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Path of Mario and Lee

Path of Luther and Stephanie