Question

A. Name the smallest angle and the largest angle of the following triangles: F 6 S 5 1. A J 5.03 7 5 G B H 5.1 2. D 4 3 E​

Answer 1

(smallest, largest) = (B, C), (D, E), (G, J)

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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ΔABC

The shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.

• smallest angle: B
• largest angle: C

ΔDEF

The shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.

• smallest angle: D
• largest angle: E

ΔGHJ

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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Additional comment

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 cannot be two angles in a triangle such that the smaller angle has the larger sine.