find ( mangle u ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n(…

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

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

Answer

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 )