Question

question 3 of 50
a triangle with sides lengths of 10, 9, and 6 is:
right
acute
obtuse

Explanation:

Step1: Recall the triangle type rule

For a triangle with sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), we use the Pythagorean theorem extension:

• If \(a^{2}+b^{2}=c^{2}\), right triangle.
• If \(a^{2}+b^{2}>c^{2}\), acute triangle.
• If \(a^{2}+b^{2}

Here, \(c = 10\), \(a = 9\), \(b = 6\).

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

Calculate \(a^{2}+b^{2}\): \(9^{2}+6^{2}=81 + 36=117\)
Calculate \(c^{2}\): \(10^{2}=100\)

Step3: Compare the two results

Since \(117>100\) (i.e., \(a^{2}+b^{2}>c^{2}\)), the triangle is acute.

Answer:

acute (the option with "acute" text)