The angle measures in a triangle are in the ratio 1:3:5. The longest side of the triangle measures 5 inches. What is the approximate perimeter of the triangle?

The angles add to 180°, so the ratio parts total 9 and each part is 20°. The triangle’s angles are therefore 20°, 60°, and 100°; the 5-inch longest side is opposite 100°. By the sine rule, the other sides are approximately 5(sin 20°/sin 100°) = 1.7 inches and 5(sin 60°/sin 100°) = 4.4 inches. The perimeter is about 5 + 1.7 + 4.4 = 11.1 inches, choice C.

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