The sides of a triangle have lengths 3, 6, and 7. What kind of triangle is it?acuterightobtuseSubmitQuestions

To determine the type of triangle, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Step 1: Identify the longest side. In this case, it's 7.

Step 2: Apply the Pythagorean theorem. If it's a right triangle, then 3² + 6² should be equal to 7².

Step 3: Calculate the squares of the sides: 3² = 9, 6² = 36, 7² = 49.

Step 4: Add the squares of the two shorter sides and compare to the square of the longest side: 9 + 36 = 45.

Step 5: Since 45 is not equal to 49, this is not a right triangle.

Step 6: If the sum of the squares of the two shorter sides is less than the square of the longest side (which it is in this case, since 45 < 49), then the triangle is obtuse.

So, the triangle with sides 3, 6, and 7 is an obtuse triangle.