Question
Determine if the following lengths make an acute, right or obtuse triangle.
7. 15, 16, 17.
7. 15, 16, 17.
Ask by Nichols Hills. in the United States
Jan 22,2025
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Tutor-Verified Answer
Answer
The triangle with sides 15, 16, and 17 is acute.
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The Deep Dive
To decide if the lengths 15, 16, and 17 form an acute, right, or obtuse triangle, you can use the triangle inequality theorem. First, check if the sum of the squares of the two shorter sides is greater than, equal to, or less than the square of the longest side. Here,
and
. Since
, this indicates an acute triangle!
Additionally, remember that the side lengths of the triangle must always adhere to the triangle inequality rule: the sum of any two sides must be greater than the third side. In this case,
,
, and
, confirming that these lengths indeed form a valid triangle.