Question

decide if the segments lengths form a triangle. if so, would the triangle be acute, right, or obtuse? 9,10,15 a. no b. yes, they would form an acute triangle. c. yes, they would form a right triangle d. yes, they would form an obtuse triangle. please select the best answer from the choices provided a b c d

Explanation:

Step1: Check triangle inequality

For three sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), the triangle inequality states \(a + b>c\). Here, \(a = 9\), \(b = 10\), \(c = 15\). So \(9 + 10=19>15\), so a triangle is formed.

Step2: Classify triangle (using Pythagorean theorem extension)

For a triangle with sides \(a\), \(b\), \(c\) (\(c\) longest), if \(a^{2}+b^{2}=c^{2}\), right; \(a^{2}+b^{2}>c^{2}\), acute; \(a^{2}+b^{2}Calculate \(9^{2}+10^{2}=81 + 100 = 181\), and \(15^{2}=225\). Since \(181<225\) (i.e., \(a^{2}+b^{2}

Answer:

D. Yes, they would form an obtuse triangle.