Question

find de.

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

Explanation:

Step1: Use trigonometric ratio

In right - triangle \(CED\), \(\tan D=\frac{CE}{DE}\). We know that \(CE = \sqrt{53}\approx7.3\) and \(D = 53^{\circ}\). The formula \(\tan D=\frac{CE}{DE}\) can be rewritten as \(DE=\frac{CE}{\tan D}\).

Step2: Substitute values

Since \(\tan53^{\circ}\approx1.33\) and \(CE=\sqrt{53}\approx7.3\), then \(DE=\frac{7.3}{1.33}\approx5.5\).

Answer:

\(5.5\)