Question

find ( mangle u ).

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

Explanation:

Step1: Identify triangle type and sides

This is a right triangle \( \triangle VWU \) with right angle at \( W \). We know \( \overline{VW} = 7.1 \) (opposite to \( \angle U \)) and \( \overline{WU} = 6.2 \) (adjacent to \( \angle U \)).

Step2: Use tangent function

The tangent of an angle in a right triangle is \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \). For \( \angle U \), \( \tan(\angle U) = \frac{VW}{WU} = \frac{7.1}{6.2} \).

Step3: Calculate the angle

First, compute \( \frac{7.1}{6.2} \approx 1.145 \). Then, take the arctangent (inverse tangent) of \( 1.145 \): \( \angle U = \arctan(1.145) \approx 48.9^\circ \).

Answer:

\( 48.9 \)