Question

simplify your answer and write it as a proper fraction, improper fraction, or whole num\\(\cos(s)=\\)

Explanation:

Step1: Find the hypotenuse of the right triangle

In right triangle \( RQS \) (right - angled at \( R \)), by the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( a = 33 \), \( b = 56 \) and \( c \) is the hypotenuse \( QS \).
So \( QS=\sqrt{33^{2}+56^{2}}=\sqrt{1089 + 3136}=\sqrt{4225}=65 \)

Step2: Recall the definition of cosine in a right triangle

For an acute angle \( \theta \) in a right triangle, \( \cos\theta=\frac{\text{adjacent side to } \theta}{\text{hypotenuse}} \)
For angle \( S \), the adjacent side is \( RS = 33 \) and the hypotenuse is \( QS=65 \)
So \( \cos(S)=\frac{RS}{QS}=\frac{33}{65} \)

Answer:

\(\frac{33}{65}\)