Question

find the sine, cosine, and tangent of $\angle e$. simplify your answers and write them as proper fractions, improper fractions, or whole numbers. $\sin(e) = \square$ $\cos(e) = \square$ $\tan(e) = \square$

Explanation:

Step1: Find side $DE$ via Pythagoras

$$DE = \sqrt{FE^2 - FD^2} = \sqrt{97^2 - 72^2} = \sqrt{9409 - 5184} = \sqrt{4225} = 65$$

Step2: Define $\sin(E)$ (opp/hyp)

$$\sin(E) = \frac{FD}{FE} = \frac{72}{97}$$

Step3: Define $\cos(E)$ (adj/hyp)

$$\cos(E) = \frac{DE}{FE} = \frac{65}{97}$$

Step4: Define $\tan(E)$ (opp/adj)

$$\tan(E) = \frac{FD}{DE} = \frac{72}{65}$$

Answer:

$\sin(E) = \frac{72}{97}$
$\cos(E) = \frac{65}{97}$
$\tan(E) = \frac{72}{65}$