Question

jamel is asked to create triangles using three of four given sticks. the sticks measure 3 in., 6 in., 7 in., and 8 in. he creates these 4 triangles. triangle 1: 3 in., 6 in., 7 in. triangle 2: 3 in., 6 in., 8 in. triangle 3: 3 in., 7 in., 8 in. triangle 4: 6 in., 7 in., 8 in. how many of his triangles are obtuse? 1 2 3 4

Explanation:

Step1: Recall the obtuse - triangle condition

For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the longest side), the triangle is obtuse if \(a^{2}+b^{2}

Step2: Check Triangle 1

Let \(a = 3\), \(b = 6\), \(c = 7\). Calculate \(a^{2}+b^{2}=3^{2}+6^{2}=9 + 36=45\) and \(c^{2}=7^{2}=49\). Since \(45<49\), Triangle 1 is obtuse.

Step3: Check Triangle 2

Let \(a = 3\), \(b = 6\), \(c = 8\). Calculate \(a^{2}+b^{2}=3^{2}+6^{2}=9 + 36=45\) and \(c^{2}=8^{2}=64\). Since \(45<64\), Triangle 2 is obtuse.

Step4: Check Triangle 3

Let \(a = 3\), \(b = 7\), \(c = 8\). Calculate \(a^{2}+b^{2}=3^{2}+7^{2}=9 + 49=58\) and \(c^{2}=8^{2}=64\). Since \(58<64\), Triangle 3 is obtuse.

Step5: Check Triangle 4

Let \(a = 6\), \(b = 7\), \(c = 8\). Calculate \(a^{2}+b^{2}=6^{2}+7^{2}=36+49 = 85\) and \(c^{2}=8^{2}=64\). Since \(85>64\), Triangle 4 is not obtuse.

Answer:

3