Determine whether each set of side lengths forms an acute, right, or obtuse triangle. (a) 4 feet, 4.5 feet,...

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Determine whether each set of side lengths forms an acute, right, or obtuse triangle.
(a) 4 feet, 4.5 feet, 7 feet
(b). 8 centimeters, 9 centimeters, 11 centimeters
(c). 9 inches, 12 inches, 15 inches
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SnapAndSolve AI · Accepted Answer

For each set, the two shorter sides sum to more than the longest side, so each forms a triangle. Compare a² + b² with c², where c is the longest side. (a) Obtuse triangle. 4² + 4.5² = 16 + 20.25 = 36.25, while 7² = 49. Since 36.25 < 49, the triangle is obtuse. (b) Acute triangle. 8² + 9² = 64 + 81 = 145, while 11² = 121. Since 145 > 121, the triangle is acute. (c) Right triangle. 9² + 12² = 81 + 144 = 225, and 15² = 225. Since the values are equal, the triangle is right.

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Determine whether each set of side lengths forms an acute, right, or obtuse triangle. (a) 4 feet, 4.5 feet,...

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