Question

what is the length of (overline{ac})? round your answer to the nearest hundredth.
2.49 units
3.62 units
4.48 units
5.36 units

Explanation:

Step1: Use cosine function in right - triangle \(ABC\)

In right - triangle \(ABC\), \(\cos A=\frac{AB}{AC}\). Given \(A = 34^{\circ}\) and \(AB = 3\) units. So, \(AC=\frac{AB}{\cos A}\).

Step2: Calculate the value of \(\cos(34^{\circ})\)

We know that \(\cos(34^{\circ})\approx0.829\).

Step3: Find the length of \(AC\)

Substitute \(AB = 3\) and \(\cos(34^{\circ})\approx0.829\) into \(AC=\frac{AB}{\cos A}\). Then \(AC=\frac{3}{0.829}\approx3.62\)

Answer:

3.62 units