Final answer:
The sine of ∠R in ΔQRS, with ∠S being 90 degrees and given side lengths, is the ratio of the side opposite ∠R (SR = 11) to the hypotenuse (RQ = 61), which is 11/61.
Step-by-step explanation:
The student is asking about the sine of ∠R in triangle QRS, where ∠S is 90 degrees, and we are given the lengths of the sides as RQ = 61, SR = 11, and QS = 60. To find the sine of ∠R, we can use the definition of sine in a right triangle, which is the length of the side opposite the angle divided by the length of the hypotenuse.
In ΔQRS, the side opposite ∠R is SR, and the hypotenuse is RQ. Therefore, the sine of ∠R is equal to the length of SR divided by the length of RQ, which is 11/61.
The ratio that represents the sine of ∠R is:
- sin(∠R) = opposite side to ∠R / hypotenuse = SR / RQ
- sin(∠R) = 11 / 61