Question

the figure below shows a wooden brace for the roof of a building. what is the value of $\sin\angle acd$?

Explanation:

Step1: Find the length of \( AC \)

By the Pythagorean theorem in \( \triangle ACD \), \( AC=\sqrt{(8 + 8)^{2}+12^{2}}=\sqrt{256 + 144}=\sqrt{400}=20\) ft.

Step2: Use the definition of sine function

In \( \triangle ACD \), \(\sin\angle ACD=\frac{AD}{AC}\). Since \( AD = 12\) ft and \( AC = 20\) ft, \(\sin\angle ACD=\frac{12}{20}=\frac{3}{5}\).

Answer:

\(\frac{3}{5}\) (the fourth option)