The sides of a triangle have lengths 2, 6, and 7. What kind of triangle is it?
a acute
b right
c obtuse
c obtuse
To determine the type of triangle, we can use the Pythagorean theorem.
Let's label the sides of the triangle as follows:
a = 2, b = 6, c = 7
Now, we can check if the triangle is a right triangle by seeing if the following equation holds true:
a^2 + b^2 = c^2
2^2 + 6^2 = 7^2
4 + 36 = 49
40 = 49
Since the equation does not hold true, we can conclude that the triangle is not a right triangle.
Next, to determine if the triangle is acute or obtuse, we can use the Law of Cosines.
If the largest side (c) is opposite the largest angle, the triangle is an obtuse triangle.
Since 7 is the largest side of the triangle, it is opposite the largest angle. Therefore, the triangle is an obtuse triangle.
So, the answer is: c) obtuse.