find ac.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nac =
find ac.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nac =
Answer
Explanation:
Step1: Identify the trigonometric ratio
In right triangle (ABC) with right angle at (A), we know the hypotenuse (BC = 7) and angle (B=35^\circ). We need to find (AC), which is the side opposite to angle (B). The sine function relates the opposite side and the hypotenuse: (\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}). So, (\sin(35^\circ)=\frac{AC}{BC}).
Step2: Substitute the known values
We know (BC = 7) and (\theta = 35^\circ). Substituting these values into the sine formula: (AC=BC\times\sin(35^\circ)).
Step3: Calculate the value
Using a calculator to find (\sin(35^\circ)\approx0.5736). Then (AC = 7\times0.5736\approx4.0152). Rounding to the nearest tenth, we get (AC\approx4.0).
Answer:
(4.0)