Question

find ce.
triangle image with right angle at c, hypotenuse de = 9, angle at d is 26°
write your answer as an integer or as a decimal rounded to the nearest tenth.
ce =

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(DCE\), for \(\angle D = 26^\circ\), \(CE\) is the opposite side, hypotenuse \(DE = 9\). Use sine:
\(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Substitute values and solve

Substitute \(\theta = 26^\circ\), hypotenuse \(=9\):
\(CE = 9 \times \sin(26^\circ)\)
Calculate \(\sin(26^\circ) \approx 0.4384\), so:
\(CE \approx 9 \times 0.4384 = 3.9456\)

Step3: Round to nearest tenth

Round \(3.9456\) to one decimal place:
\(CE \approx 3.9\)

Answer:

\(3.9\)