Question

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

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle T\), the adjacent side to \(\angle T\) is \(TU = 4\) and the hypotenuse is \(TS=10\). So, \(\cos T=\frac{TU}{TS}\).

Step2: Calculate \(\cos T\)

Substitute \(TU = 4\) and \(TS = 10\) into the formula: \(\cos T=\frac{4}{10}=0.4\).

Step3: Find \(\angle T\)

Take the inverse cosine of \(0.4\). Using a calculator, \(T=\cos^{-1}(0.4)\approx66.4^{\circ}\).

Answer:

\(66.4\)