Question

In AQRS, the measure of <S=90°, RQ = 97, QS = 72, and SR = 65. What ratio represents the tangent of <R?​

Answer 1

The ratio representing the tangent of angle R in triangle AQRS is 72/65, calculated using the tangent function's definition in right-angled triangles.

Step-by-step explanation:

To find the ratio representing the tangent of (tan R) in triangle AQRS, we use the definition of the tangent function in right-angled triangles. The tangent of an angle in a right-angled triangle is the ratio of the side opposite the angle to the side adjacent to the angle (tan θ = opposite/adjacent). Since is 90°, this is a right triangle, and the side opposite is QS which measures 72, and the side adjacent to is SR, which measures 65. Therefore, the tangent of is:

tan R = QS / SR

tan R = 72 / 65

So, the ratio representing the tangent of is 72/65.