Question

find ( mangle v ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle v=) ( circ )

Explanation:

Step1: Identify trigonometric ratio

In right - triangle \( \triangle UVW\), we know the hypotenuse \(UV = 9.6\) and the adjacent side to \(\angle V\) is \(VW=4.3\). We use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos V=\frac{VW}{UV}\).

Step2: Substitute values

Substitute \(VW = 4.3\) and \(UV = 9.6\) into the formula: \(\cos V=\frac{4.3}{9.6}\).

Step3: Calculate the value of \(\cos V\)

\(\frac{4.3}{9.6}\approx0.4479\).

Step4: Find the angle \(V\)

Take the inverse cosine (arccos) of \(0.4479\). \(V=\cos^{- 1}(0.4479)\). Using a calculator, \(V\approx63.4^{\circ}\).

Answer:

\(63.4\)