Which set of numbers can represent the side lengths, in inches, of an acute triangle? 4, 5, 75, 7, 86, 7, 107, 9, 12

Second set (5,7 and 8)

Explanation:
Triangles can be classified based on their side lengths as follows:
1- (longest side)² = (first short side)² + (second short side)² > right Δ
2- (longest side)² > (first short side)² + (second short side)² > obtuse Δ
1- (longest side)² < (first short side)² + (second short side)² > acute Δ

let's perform this check on the given sets:
1- First set (4,5 and 7):
7² = 49
5² = 25
4² = 16
49 > 25 + 16
49 > 41
Triangle is obtuse

2- Second set (5,7 and 8):
8² = 64
7² = 49
5² = 25
64 < 49 + 25
64 < 74
Triangle is acute

3- Third set (6,7 and 10):
10² = 100
7² = 49
6² = 36
100 > 49 + 36
100 > 85
Triangle is obtuse

4- Fourth set (7,9 and 12):
12² = 144
9² = 81
7² = 49
144 > 81 + 49
144 > 130
Triangle is obtuse

Hope this helps :)

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