Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \(ABC\) with \(\angle C = 90^\circ\), \(\angle A = 49^\circ\), and \(BC = 4.6\). We can use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan(49^\circ)=\frac{BC}{AC}\), so we can solve for \(AC\) as \(AC = \frac{BC}{\tan(49^\circ)}\).

Step2: Substitute the values

We know \(BC = 4.6\) and \(\tan(49^\circ)\approx1.1504\). So \(AC=\frac{4.6}{\tan(49^\circ)}\approx\frac{4.6}{1.1504}\).

Step3: Calculate the value

\(\frac{4.6}{1.1504}\approx4.0\) (rounded to the nearest tenth).

Answer:

\(4.0\)