Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\), we know the hypotenuse \(AC = 7\) and we want to find the side \(AB\). The angle \(\angle C=46^{\circ}\). We use the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 46^{\circ}\), the opposite side to \(\angle C\) is \(AB\), and the hypotenuse \(AC = 7\). So, \(\sin(46^{\circ})=\frac{AB}{AC}\).

Step2: Solve for \(AB\)

Since \(AC = 7\), we can rewrite the formula as \(AB=AC\times\sin(46^{\circ})\). We know that \(\sin(46^{\circ})\approx0.7193\). Then \(AB = 7\times0.7193=5.0351\approx5.0\) (rounded to the nearest tenth).

Answer:

$5.0$