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 trigonometric ratio

We have a right - triangle \( \triangle TSU \) with \( \angle S = 90^{\circ} \), \( TS = 7.2 \), and \( SU = 2.5 \). To find \( m\angle U \), 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 \( \angle U \), the opposite side is \( TS \) and the adjacent side is \( SU \). So, \( \tan(\angle U)=\frac{TS}{SU} \).

Step2: Substitute the values and calculate the angle

Substitute \( TS = 7.2 \) and \( SU = 2.5 \) into the tangent formula: \( \tan(\angle U)=\frac{7.2}{2.5}=2.88 \). Then, to find \( \angle U \), we take the arctangent (inverse tangent) of 2.88. So, \( \angle U=\arctan(2.88) \). Using a calculator, we find that \( \angle U\approx70.9^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 70.9 \)