Question

select the correct answer from each drop - down menu. use the figure to complete the following statements. sin(f) = cos(f) = sin(g) = cos(g) =

Explanation:

Step1: Recall sine and cosine definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Find $\sin(F)$

For angle $F$, the opposite side to $F$ is $HG = 3$ and the hypotenuse is $FG=5$. So, $\sin(F)=\frac{3}{5}$.

Step3: Find $\cos(F)$

For angle $F$, the adjacent side to $F$ is $FH = 4$ and the hypotenuse is $FG = 5$. So, $\cos(F)=\frac{4}{5}$.

Step4: Find $\sin(G)$

For angle $G$, the opposite side to $G$ is $FH=4$ and the hypotenuse is $FG = 5$. So, $\sin(G)=\frac{4}{5}$.

Step5: Find $\cos(G)$

For angle $G$, the adjacent side to $G$ is $HG=3$ and the hypotenuse is $FG = 5$. So, $\cos(G)=\frac{3}{5}$.

Answer:

$\sin(F)=\frac{3}{5}$, $\cos(F)=\frac{4}{5}$, $\sin(G)=\frac{4}{5}$, $\cos(G)=\frac{3}{5}$