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: Find the hypotenuse \( CD \)

In right triangle \( CDE \), by Pythagorean theorem \( CD^2 = DE^2 + CE^2 \). Given \( DE = 77 \), \( CE = 36 \), so \( CD^2 = 77^2 + 36^2 = 5929 + 1296 = 7225 \), then \( CD = \sqrt{7225} = 85 \).

Step2: Calculate \( \sin(C) \)

\( \sin(C) = \frac{\text{opposite to } \angle C}{\text{hypotenuse}} = \frac{DE}{CD} = \frac{77}{85} \).

Step3: Calculate \( \cos(C) \)

\( \cos(C) = \frac{\text{adjacent to } \angle C}{\text{hypotenuse}} = \frac{CE}{CD} = \frac{36}{85} \).

Step4: Calculate \( \tan(C) \)

\( \tan(C) = \frac{\text{opposite to } \angle C}{\text{adjacent to } \angle C} = \frac{DE}{CE} = \frac{77}{36} \).

Answer:

\( \sin(C) = \frac{77}{85} \)
\( \cos(C) = \frac{36}{85} \)
\( \tan(C) = \frac{77}{36} \)