Question

find rs.
(there is a right triangle rst with right angle at r, angle at s is 60 degrees, and hypotenuse ts = 20)
write your answer in simplified, rationalized form. do not round.
rs =

Explanation:

Step1: Identify triangle type

Triangle \( RST \) is right - angled at \( R \), with \( \angle S = 60^\circ \) and hypotenuse \( TS=20 \). We use trigonometric ratios. In a right - triangle, \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle S = 60^\circ \), the adjacent side to \( \angle S \) is \( RS \) and the hypotenuse is \( TS \).

Step2: Apply cosine ratio

We know that \( \cos(60^\circ)=\frac{RS}{TS} \). We know that \( \cos(60^\circ)=\frac{1}{2} \) and \( TS = 20 \). Substituting these values into the formula: \( \frac{1}{2}=\frac{RS}{20} \).

Step3: Solve for \( RS \)

To solve for \( RS \), we cross - multiply. So, \( RS=20\times\frac{1}{2} = 10 \).

Answer:

\( 10 \)