Question

1 matching 20 points given the following, match the trig function to its correct ratio: image.png 15/17 15/8 8/15 17/15 8/17 17/8 sinθ = tanθ = cosθ =

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\)
For the given right - triangle with \(\theta\), the opposite side \(= 8\), the adjacent side \(= 15\), and the hypotenuse \(= 17\)

Step2: Calculate \(\sin\theta\)

Using the formula \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), we substitute the values: \(\sin\theta=\frac{8}{17}\)

Step3: Calculate \(\tan\theta\)

Using the formula \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), we substitute the values: \(\tan\theta=\frac{8}{15}\)

Step4: Calculate \(\cos\theta\)

Using the formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), we substitute the values: \(\cos\theta=\frac{15}{17}\)

Answer:

\(\sin\theta=\frac{8}{17}\), \(\tan\theta=\frac{8}{15}\), \(\cos\theta=\frac{15}{17}\)