Question

find the cosine of ∠c.
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
cos (c) =

Explanation:

Step1: Identify the sides relative to ∠C

In right triangle \( CDB \), \( \angle D = 90^\circ \). For \( \angle C \), the adjacent side is \( CD = 48 \), the opposite side is \( BD = 55 \), and the hypotenuse \( CB \) can be found using the Pythagorean theorem: \( CB=\sqrt{CD^{2}+BD^{2}} \).

Step2: Calculate the hypotenuse

\( CB = \sqrt{48^{2}+55^{2}}=\sqrt{2304 + 3025}=\sqrt{5329}=73 \)

Step3: Use the cosine definition

The cosine of an angle in a right triangle is defined as \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle C \), adjacent side is \( 48 \), hypotenuse is \( 73 \). So \( \cos(C)=\frac{48}{73} \)

Answer:

\( \frac{48}{73} \)