Question

the picture shows a barn door.
what is the length of the bar ac? (1 point)

\\(6 \sin 60^\circ\\)

\\(6 \cos 60^\circ\\)

\\(\frac{6}{\cos 60^\circ}\\)

\\(\frac{6}{\tan 60^\circ}\\)

Explanation:

Identify the right triangle and given values

The barn door features a right triangle \(ABC\) with a right angle at \(C\).
The vertical side \(BC\) has a length of \(6\text{ feet}\).
The angle \(\angle BAC\) is given as \(60^\circ\).

Apply the tangent ratio

The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side:

$$ \tan(60^\circ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{BC}{AC} $$

Solve for the length of AC

Substitute the known value \(BC = 6\) into the equation and solve for \(AC\):

$$ \tan(60^\circ) = \frac{6}{AC} \implies AC = \frac{6}{\tan(60^\circ)} $$

Answer:

• (A) \(6 \sin 60^\circ\)
• (B) \(6 \cos 60^\circ\)
• (C) \(\frac{6}{\cos 60^\circ}\)
• (D) \(\frac{6}{\tan 60^\circ}\) (Correct answer)