To find the order of the angle measures from smallest to largest, let's look at the given diagram and notice the marked lengths of the sides.
Looking at the diagram, we can see that m∠ Z = 90^(∘). Therefore, △ WYZ is a right triangle. To order the sides from smallest to largest, let's first find the length of the hypotenuse using the Pythagorean Theorem.
YW^2 = ZY^2 + WZ^2We will substitute ZY= 2.3 and WZ= 3.4 into the equation.
The length of the hypotenuse is about 4.1. From here, we can order the sides as follows.
ZY < WZ < YW
⇕
2.3 < 3.4 < 4.1
Next, let's consider Theorem 5.9 about Angle-Side Relationships in Triangles.
Angle-Side Relationships in Triangles
If one side of a triangle is longer than another side, then the angle opposite the longer side has greater measure than the angle opposite the shorter side.
Now we need to think about the sides, and the corresponding opposite angles.
cc
Side & Opposite Angle [0.5em]
ZY & ∠ W [0.5em]
WZ & ∠ Y [0.5em]
YW & ∠ Z
Therefore, we can list angles in order from smallest to largest.
m∠ W < m∠ Y < m∠ Z
