Final answer:
To find the tangents of acute angles R and S in a right triangle, we would need the lengths of the sides opposite and adjacent to the respective angles. The tangent is the ratio of these two sides, and without specific lengths, we cannot provide an exact answer. We would choose the option that best matches the side lengths given to their corresponding tangent values.
Step-by-step explanation:
The question concerns the calculation of the tangents of the acute angles in a right triangle. The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. To find the correct values for the tangents of angles R and S, we must have the lengths of the sides that are opposite and adjacent to these angles.
Step-by-Step Explanation
- Let R be one of the acute angles in the right triangle. The side opposite angle R is typically denoted as opposite side to R or O, and the side adjacent to R is noted as adjacent side to R or A.
- The tangent of R, denoted by tan R, is the ratio O/A.
- Similarly, for the other acute angle S, the side opposite S is the adjacent side to R and the side adjacent to S is the opposite side to R.
- The tangent of S, tan S, is the ratio of the opposite side to R over the adjacent side to R. Without specific side lengths, we cannot solve for the exact values.
- However, based on the options provided and assuming the sides mentioned correspond to the ratios given, we can match the lengths to the correct tangent values.
Therefore, assuming that the lengths given in the ratios are correct, the option that has the tangent values as the correct ratios of the sides would be the answer. Given the ratios provided, the lengths of the sides have been used to calculate the tangents in a right triangle.