No, the catheti of a right-angled triangle can be calculated without needing to know the length of the hypotenuse. The catheti are the two shorter sides of the right-angled triangle, and their lengths can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, the catheti can be calculated using the lengths of the other sides of the triangle without needing to know the length of the hypotenuse. **

When only the hypotenuse is given in a right-angled triangle, it is not possible to determine the lengths of the other two sides without additional information. This is because there are an infinite number of right-angled triangles with the same hypotenuse but different side lengths. In order to find the lengths of the other sides, either the length of one of the other sides or the measure of one of the non-right angles must be given. **

Yes, in a right-angled triangle, the hypotenuse is always represented by the letter 'c' in the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides. This relationship is always true for any right-angled triangle, making the hypotenuse always represented by 'c' in the theorem. **

The legs of a right-angled triangle are the two sides that form the right angle. The hypotenuse is the side opposite the right angle and is the longest side of the triangle. In a right-angled triangle, the relationship between the lengths of the legs and the hypotenuse is given by the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs. **

In a right triangle, the base is the side that is perpendicular to the vertical height of the triangle. It is the side on which the triangle rests. The hypotenuse is the longest side of the right triangle and is opposite the right angle. It is the side that is directly across from the right angle. **

No, a right-angled triangle cannot be solved only with the hypotenuse given. In order to solve a right-angled triangle, at least one of the other sides must be known. This is because the hypotenuse alone does not provide enough information to determine the lengths of the other sides or the angles of the triangle. Additional information, such as the length of one of the other sides or one of the angles, is needed to solve the triangle. **

No, in a right triangle, if the hypotenuse and another angle are given, we can determine the lengths of all three sides using trigonometric ratios. The hypotenuse is the side opposite the right angle, and the other given angle helps determine the relationship between the sides of the triangle. With this information, we can use trigonometry to find the lengths of the other two sides. **

To calculate the length of the legs of a right-angled triangle when only the hypotenuse is given, you can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, if you know the length of the hypotenuse, you can use this formula to solve for the lengths of the legs. Simply rearrange the formula to solve for the length of one of the legs, and then use that value to solve for the other leg. **