In a right triangle, if you know the measures of both acute angles, you can determine the lengths of the sides using trigonometric ratios. There are three main ratios: sine, cosine, and tangent. If you know one acute angle and the length of one side, you can use sine, cosine, or tangent to find the lengths of the other sides. For instance, cosine is used when the known side is adjacent to the given angle, sine is used when the known side is opposite the given angle, and tangent is employed when both sides adjacent to the angle are known. Once you've determined the lengths of two sides, you can apply the Pythagorean theorem to find the length of the third side, completing the triangle. Thus, knowing the measures of both acute angles enables you to ascertain the lengths of all three sides of the right triangle.
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When dealing with a right triangle, the lengths of the sides can be determined by knowing the measures of the acute angles and using trigonometric ratios. The three main ratios that are used are sine, cosine, and tangent. If one acute angle and the length of one side are known, any of these ratios can be utilized to find the lengths of the other sides. For example, cosine is used when the known side is adjacent to the given angle, sine is used when the known side is opposite the given angle, and tangent is used when both sides adjacent to the angle are known. Once the lengths of two sides are determined, the Pythagorean theorem can be applied to find the length of the third side, thereby completing the triangle. Thus, having knowledge of both acute angles allows for the determination of the lengths of all three sides of the right triangle.
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