Question

triangle vwx is a right triangle.
match each trigonometric expression with its value. values may be used more than once or not at all.
\\( \begin{array} { l l l l l l } { \frac { 8 } { 17 } } & { \frac { 8 } { 15 } } & { \frac { 15 } { 17 } } & { \frac { 17 } { 15 } } & { \frac { 15 } { 8 } } & { \frac { 17 } { 8 } } end{array} \\)
\\( \begin{array} { l } { cos ( v ) } \\\\ { cos ( w ) } \\\\ { sin ( v ) } \\\\ { sin ( w ) } \\\\ { \tan ( v ) } end{array} \\)

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)

Step2: Find \(\cos(V)\)

For angle \(V\), adjacent side \( = 15\), hypotenuse \(=17\). So \(\cos(V)=\frac{15}{17}\)

Step3: Find \(\cos(W)\)

For angle \(W\), adjacent side \( = 8\), hypotenuse \(=17\). So \(\cos(W)=\frac{8}{17}\)

Step4: Find \(\sin(V)\)

For angle \(V\), opposite side \( = 8\), hypotenuse \(=17\). So \(\sin(V)=\frac{8}{17}\)

Step5: Find \(\sin(W)\)

For angle \(W\), opposite side \( = 15\), hypotenuse \(=17\). So \(\sin(W)=\frac{15}{17}\)

Step6: Find \(\tan(V)\)

For angle \(V\), opposite side \( = 8\), adjacent side \(=15\). So \(\tan(V)=\frac{8}{15}\)

Answer:

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