Question

In AQRS, the measure of ∠S=90°, RQ = 85, SR = 36, and QS = 77. What ratio represents the cosecant of ∠Q?

a. R
b. 85
c. 36
d. s
e. 77

Answer 1

The ratio representing the cosecant of ∠Q in the right-angled triangle AQRS with given sides is the reciprocal of the sine of the angle, which is 85/36. Thus, the correct answer is option (c) which is 36.

Step-by-step explanation:

The student has asked about the ratio that represents the cosecant of ∠Q in triangle AQRS. Given that ∠S is 90°, and the lengths of the sides RQ, SR, and QS are 85, 36, and 77 respectively, we are looking for the cosecant of ∠Q. The cosecant of an angle in a right-angled triangle is the reciprocal of the sine, which is the ratio of the length of the hypotenuse to the length of the opposite side. Since ∠Q is opposite the side SR and the hypotenuse RQ is the longest side, we have cosecant ∠Q = RQ / SR.

By substituting the known values, cosecant ∠Q is equal to 85 / 36. Therefore, the correct answer for the cosecant of ∠Q in this scenario is 36, which corresponds to choice (c).