Answer:
(smallest, largest) = (B, C), (D, E), (G, J)
Step-by-step explanation:
Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.
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<h3>ΔABC</h3>
The shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.
- smallest angle: B
- largest angle: C
<h3>ΔDEF</h3>
The shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.
- smallest angle: D
- largest angle: E
<h3>ΔGHJ</h3>
The shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.
- smallest angle: G
- largest angle: J
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<em>Additional comment</em>
Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there <em>cannot be two angles in a triangle such that the smaller angle has the larger sine</em>.
