Question

sin r = cos r = tan r = name 1. label: opposite, adjacent, hypotenuse 2. use your labels to write the trig ratios for sin, cos, and tan of the given angle.

Explanation:

Step1: Identify opposite, adjacent, hypotenuse for angle \(R\)

For angle \(R\), the side opposite is \(QS = 40\), the side adjacent is \(RQ=9\), and the hypotenuse is \(RS = 41\).

Step2: Calculate \(\sin R\)

Using the formula \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), we have \(\sin R=\frac{QS}{RS}=\frac{40}{41}\)

Step3: Calculate \(\cos R\)

Using the formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), we have \(\cos R=\frac{RQ}{RS}=\frac{9}{41}\)

Step4: Calculate \(\tan R\)

Using the formula \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), we have \(\tan R=\frac{QS}{RQ}=\frac{40}{9}\)

Answer:

\(\sin R=\frac{40}{41}\), \(\cos R=\frac{9}{41}\), \(\tan R=\frac{40}{9}\)