find the sine, cosine, and tangent of ∠f.\nsimplify your answers and write them as proper fractions…

Answer:

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

Explanation:

Step1: Find the length of the adjacent side

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$. Let the hypotenuse $c = 5$ and one - side $b = 4$. Then the adjacent side $a=\sqrt{5^{2}-4^{2}}=\sqrt{25 - 16}=\sqrt{9}=3$.

Step2: Recall the sine formula

The sine of an angle in a right - triangle is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle F$, the opposite side to $\angle F$ is $DE = 4$ and the hypotenuse $DF=5$. So $\sin(F)=\frac{4}{5}$.

Step3: Recall the cosine formula

The cosine of an angle in a right - triangle is $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle F$, the adjacent side to $\angle F$ is $EF = 3$ and the hypotenuse $DF = 5$. So $\cos(F)=\frac{3}{5}$.

Step4: Recall the tangent formula

The tangent of an angle in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle F$, the opposite side is $4$ and the adjacent side is $3$. So $\tan(F)=\frac{4}{3}$.