jamel is asked to create triangles using three of four given sticks. the sticks measure 3 in., 6 in., 7 in…

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

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

Answer

Answer:

C. 3

Explanation:

Step1: Recall the Pythagorean - related rule for obtuse - angled triangles

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

Step2: Check Triangle 1

The side lengths are (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

The side lengths are (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

The side lengths are (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

The side lengths are (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.

So, the number of obtuse - angled triangles is 3.