Question

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

Explanation:

Step1: Calculate side ED

Use Pythagorean theorem: $ED = \sqrt{CD^2 - CE^2}$
$ED = \sqrt{52^2 - 20^2} = \sqrt{2704 - 400} = \sqrt{2304} = 48$

Step2: Find $\sin(C)$

Opposite over hypotenuse: $\sin(C) = \frac{ED}{CD}$
$\sin(C) = \frac{48}{52} = \frac{12}{13}$

Step3: Find $\cos(C)$

Adjacent over hypotenuse: $\cos(C) = \frac{CE}{CD}$
$\cos(C) = \frac{20}{52} = \frac{5}{13}$

Step4: Find $\tan(C)$

Opposite over adjacent: $\tan(C) = \frac{ED}{CE}$
$\tan(C) = \frac{48}{20} = \frac{12}{5}$

Answer:

$\sin(C) = \frac{12}{13}$
$\cos(C) = \frac{5}{13}$
$\tan(C) = \frac{12}{5}$