Question

find ( mangle v ).

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

( mangle v=square^{circ} )

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(WUV\), \(\tan V=\frac{opposite}{adjacent}\). The side opposite to \(\angle V\) is \(WU = 7\), and the side adjacent to \(\angle V\) is \(UV=4\). So, \(\tan V=\frac{7}{4}\).

Step2: Use the inverse tangent function

We know that if \(\tan\theta = x\), then \(\theta=\tan^{- 1}(x)\). Here, \(V = \tan^{-1}(\frac{7}{4})\).
Using a calculator, \(\tan^{-1}(\frac{7}{4})=\tan^{-1}(1.75)\approx60.3^{\circ}\)

Answer:

\(60.3\)