Question

find ce.

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

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle \(CDE\), right-angled at \(D\). We know \(\angle C = 32^\circ\), opposite side to \(\angle C\) is \(ED = 1.9\), and \(CE\) is the hypotenuse. Use sine function:
\(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Substitute known values

Substitute \(\theta = 32^\circ\), opposite \(= 1.9\), hypotenuse \(= CE\):
\(\sin(32^\circ) = \frac{1.9}{CE}\)

Step3: Solve for \(CE\)

Rearrange to isolate \(CE\):
\(CE = \frac{1.9}{\sin(32^\circ)}\)
Calculate \(\sin(32^\circ) \approx 0.5299\), so:
\(CE \approx \frac{1.9}{0.5299} \approx 3.6\)

Answer:

3.6