Question

find ce.
write your answer as an integer or as a decimal rounded to the nearest tenth.
ce =

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( CDE \), we know angle \( C = 63^\circ \), side \( CD = 3 \) (adjacent to angle \( C \)), and we need to find \( CE \) (hypotenuse). The cosine ratio is defined as \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(63^\circ)=\frac{CD}{CE} \).

Step2: Solve for \( CE \)

Rearranging the formula for \( CE \), we get \( CE = \frac{CD}{\cos(63^\circ)} \). Substituting \( CD = 3 \) and \( \cos(63^\circ)\approx0.4540 \), we have \( CE=\frac{3}{0.4540}\approx6.6 \).

Answer:

\( 6.6 \)