Question

A classmate drew an acute triangle with sides 9 in. and 12 in. What is the greatest possible whole number that can be the length of the longest side o

Right triangles and trigonometry
ANSWERED
asked 2021-06-03
A classmate drew an acute triangle with sides 9 in. and 12 in. What is the greatest possible whole number that can be the length of the longest side of the triangle in inches? Provide evidence.

Expert Answers (1)

2021-06-04

By the Pythagorean Inequality Theorem, a triangle is acute if \(a2+b2>c2a\) where c is the longest side. So, we can write
\(\displaystyle{9}^{{2}}+{12}^{{2}}{>}{c}^{{2}}\)
\(\displaystyle{81}+{144}{>}{c}^{{2}}\)
\(\displaystyle{225}{>}{c}^{{2}}\)
\(\displaystyle{15}{>}{c}\)
This means that the longest side must be less than 15 inches. Hence, the e greatest possible whole number that can be the length of the longest side of the triangle is 14 inches.

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