Question

find vw.
v 5.6 x
51°
w
write your answer as an integer or as a decimal rounded to the nearest tenth.
vw =
submit

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(VXW\), we know the adjacent side \(VX = 5.6\) to the angle \(\angle V=51^{\circ}\), and we want to find the hypotenuse \(VW\). We use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), where \(\theta = 51^{\circ}\), adjacent \(=VX\), and hypotenuse \(=VW\). So, \(\cos(51^{\circ})=\frac{VX}{VW}\).

Step2: Solve for \(VW\)

Rearrange the formula \(\cos(51^{\circ})=\frac{VX}{VW}\) to get \(VW=\frac{VX}{\cos(51^{\circ})}\).
Substitute \(VX = 5.6\) into the formula. We know that \(\cos(51^{\circ})\approx0.6293\).
Then \(VW=\frac{5.6}{0.6293}\).

Step3: Calculate the value

\(VW=\frac{5.6}{0.6293}\approx8.9\)

Answer:

\(8.9\)