A triangle has sides that measure 2 inches, 7 inches, and 1 inch. Will it be acute, obtuse, or right?
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If it's a right triangle, 7^2 = 2^2 + 1^2
that is clearly false.
Since 7^2 > 2^2 + 1^2 the triangle is obtuse.
the triangle doesn't exist
the two shorter sides aren't enough to "close up" the triangle
To determine whether a triangle is acute, obtuse, or right, we need to compare the lengths of its sides.
In this case, we have a triangle with sides measuring 2 inches, 7 inches, and 1 inch.
To classify the 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 other two sides.
Let's calculate the squares of the side lengths:
2^2 = 4
7^2 = 49
1^2 = 1
Now, let's check if the sum of the squares of the two shorter sides is greater than the square of the longest side:
4 + 1 = 5
Since 5 is less than the square of the longest side (49), we can conclude that the triangle is acute.