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 triangle type and trigonometric ratio

This is a right - triangle \( \triangle UVW \) with \( \angle W = 90^{\circ} \), \( UW = 4 \), and \( VW = 8 \). To find \( m\angle V \), we can use the tangent function. The tangent of an angle in a right - triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For \( \angle V \), the opposite side is \( UW = 4 \) and the adjacent side is \( VW = 8 \). So, \( \tan(V)=\frac{UW}{VW}=\frac{4}{8} = 0.5 \).

Step2: Calculate the angle

To find the measure of \( \angle V \), we take the arctangent (inverse tangent) of \( 0.5 \). Using a calculator, \( m\angle V=\arctan(0.5) \). Calculating this, we get \( m\angle V\approx26.6^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 26.6 \)