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

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

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

Answer

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right triangle ( \triangle UVT ) with right angle at ( T ). To find ( m\angle V ), we can use the sine function, since ( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} ). Here, the side opposite ( \angle V ) is ( UT = 7.2 ) and the hypotenuse is ( UV = 8.4 ). So, ( \sin(\angle V)=\frac{UT}{UV}=\frac{7.2}{8.4} ).

Step2: Calculate the angle

First, simplify ( \frac{7.2}{8.4}=\frac{72}{84}=\frac{6}{7}\approx0.8571 ). Then, take the inverse sine (arcsin) of ( 0.8571 ) to find ( \angle V ). Using a calculator, ( \angle V=\arcsin\left(\frac{7.2}{8.4}\right)\approx\arcsin(0.8571)\approx59.0^\circ ) (rounded to the nearest tenth).

Answer:

( 59.0 )