Question

find the sine, cosine, and tangent of ∠f. simplify your answers and write them as proper fractions, improper fractions, or whole numbers. sin (f) = cos (f) = tan (f) =

Explanation:

Step1: Find side FE (Pythagoras)

$$FE = \sqrt{FD^2 - DE^2} = \sqrt{73^2 - 55^2} = \sqrt{5329 - 3025} = \sqrt{2304} = 48$$

Step2: Define sin(F) (opp/hyp)

$\sin(F) = \frac{DE}{FD} = \frac{55}{73}$

Step3: Define cos(F) (adj/hyp)

$\cos(F) = \frac{FE}{FD} = \frac{48}{73}$

Step4: Define tan(F) (opp/adj)

$\tan(F) = \frac{DE}{FE} = \frac{55}{48}$

Answer:

$\sin(F) = \frac{55}{73}$
$\cos(F) = \frac{48}{73}$
$\tan(F) = \frac{55}{48}$