Question

find the length of \\( \overline{bc} \\) in the figure.
hint: use the pythagorean theorem to find \\( x \\). remember, you can use a calculator for this lesson.

Explanation:

Step1: Find the length of \( EC \)

Since \( EA = 8 \) and \( AD = 6 + BD \), and \( EADC \) is a rectangle, \( EC=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}=10 \).

Step2: Use trigonometric ratio to find \( y\) (i.e., \( BC \))

In right - triangle \( BDC \), \(\sin(36.9^{\circ})=\frac{BD}{EC}\), \(BD = 8\), \(EC = 10\). Also, using \(\cos(36.9^{\circ})=\frac{y}{EC}\).
Since \(\cos(36.9^{\circ})\approx0.8\) and \(EC = 10\), then \(y=EC\times\cos(36.9^{\circ})\).
\(y = 10\times0.8=6\).

Answer:

\(6\)