find ab.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nab =
find ab.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nab =
Answer
Answer:
$5.0$
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).