George said that if he had a diagram that showed the measure of one acute angle and the length of one side of a right triangle, he could find the measure of the other acute angle and the lengths of the other sides. Is he right? Explain.
Yes, George is correct. In a right triangle, the sum of the measures of the acute angles is always 90 degrees. Therefore, if we know the measure of one acute angle, we can subtract it from 90 degrees to find the measure of the other acute angle.
Additionally, if we know the length of one side of a right triangle, we can use trigonometric ratios (such as sine, cosine, or tangent) to find the lengths of the other sides. For example, if we know the length of the side adjacent to a given acute angle, we can use the cosine ratio to find the length of the hypotenuse, and then use the Pythagorean theorem to find the length of the other side.
Therefore, if George has a diagram that shows the measure of one acute angle and the length of one side of a right triangle, he can indeed find the measure of the other acute angle and the lengths of the other sides.