Question

find ( mangle w ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle w=square^{circ} )

Explanation:

Step1: Identify the sides relative to angle \(W\)

In right - triangle \(VWU\), \(WU = 2\) (adjacent side to \(\angle W\)) and \(VU = 5\) (opposite side to \(\angle W\)).

Step2: Use the tangent function

The tangent of an angle in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan W=\frac{VU}{WU}\).
Substitute \(VU = 5\) and \(WU = 2\) into the formula: \(\tan W=\frac{5}{2}=2.5\).

Step3: Find the angle using the inverse tangent function

If \(\tan W = 2.5\), then \(W=\tan^{- 1}(2.5)\).
Using a calculator, \(W\approx68.2^{\circ}\).

Answer:

\(68.2\)