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 the trigonometric ratio

In right - triangle \(TUV\) with \(\angle T = 90^{\circ}\), we know the adjacent side to \(\angle U\) (\(TU = 9\)) and the hypotenuse (\(UV=10\)). We use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos\angle U=\frac{TU}{UV}\).

Step2: Substitute the values

Substitute \(TU = 9\) and \(UV = 10\) into the cosine formula. We get \(\cos\angle U=\frac{9}{10}=0.9\).

Step3: Find the angle

To find \(\angle U\), we use the inverse cosine function. \(\angle U=\cos^{- 1}(0.9)\). Using a calculator, \(\cos^{-1}(0.9)\approx25.8^{\circ}\).

Answer:

$25.8^{\circ}$