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Can the numbers 24 32 40 be the lengths of the three sides of a right triangle?
Yes because they comply with Pythagoras' theorem for a right angle triangle
How do you find the length of hypotenuse when the right triangle has an altitude?
All triangles have an altitude. In fact they all have three of them. Whether or not they have an altitude, the important thing when trying to determine the length of the hypotenuse is what information you have on the lengths of the sides. Altitudes, medians can help determine the lengths of sides, as can angles. You need a minimum of 3 pieces of information. There is only one in the question: the fact that the triangle has a right angle.
How do you determine that the triangle is a right triangle through the 3 vertices?
If one of the three interior angles is 90 degrees then it is a right triangle.
How can you determine whether a triangle is a right triangle if you only have the lengths of its three sides?
The pathagoren theorm states that a2+ b2 = c2. If you put your lenghts into the equation and it comes out true (100=100), then the triangle is a right trianlge. If it is a false equation (100=30), then it is not a right triangle. Where a = lenght of leg 1, b = lenght of leg 2, and c = lenght of hypotenuse.
What type of triangle is ABC?
You must have more information about the triangle. If you know the angles, and two of them are equal, it is an isosceles triangle. If all three of the angles are sixty-degrees, it is an equilateral triangle. If none of the angles are the same, it is a scalene triangle. If one of the angles is ninety degrees, it is a right triangle (right triangles may also be scalene or isosceles). If you know the side lengths and two of them are equal, it is isosceles. If they are all equal, it is equilateral. If none of them are equal, it is scalene. A scalene or isosceles triangle may also be a right triangle, which you could determine from side lengths using the pythagorean theorem.
