Answer: To determine whether a triangle is acute, right, or obtuse, we need to compare the lengths of its sides to the measure of its angles. The triangle is acute if all three angles measure less than 90 degrees, it is right if one angle measures exactly 90 degrees, and it is obtuse if one angle measures more than 90 degrees.
In the case of a triangle with sides 3, radical7, and 4, we can use the Pythagorean theorem to find the measure of its angles. The theorem 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.
Since we know that one side of the triangle has length 4, and another side has length radical7, we can use the theorem to find the length of the third side, which is the hypotenuse. We can write this as an equation: 4^2 + radical7^2 = x^2, where x is the length of the hypotenuse. Solving for x, we get x = 5.
Since the length of the hypotenuse is 5, and one of the other sides has length 4, we can conclude that this triangle is a right triangle. Therefore, the triangle is a right triangle and not acute or obtuse.