Answer: [tex]QS=11.8cm[/tex]
Step-by-step explanation:
1. You have the following information:
- The lenght of [tex]RS[/tex] is 2 centimeters.
- The angle m∠S=80°.
- Cos80°=0.17
2. Therefore, you can calculate the lenght of the segment [tex]QS[/tex] as following:
[tex]cos80=\frac{adjacent}{hypotenuse}[/tex]
[tex]adjacent=2cm\\hypotenuse=QS\\cos80=0.17[/tex]
3. Substitute values and solve for [tex]QS[/tex]:
[tex]0.17=\frac{2cm}{QS}\\QS=\frac{2cm}{0.17} \\QS=11.76cm[/tex]
4. To the nearest tenth:
[tex]QS=11.8cm[/tex]
