Answer:
11. x = 32.6°
12. x = 27.0
Step-by-step explanation:
Question 11
[tex]\sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}[/tex]
Given:
- [tex]\theta[/tex] = x
- side opposite angle = 7
- hypotenuse = 13
[tex]\implies \sin(x)=\dfrac{7}{13}[/tex]
[tex]\implies x=\sin^{-1}\left(\dfrac{7}{13}\right)[/tex]
[tex]\implies x=32.6\textdegree \textsf{ (nearest tenth)}[/tex]
Question 12
[tex]\sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}[/tex]
Given:
- [tex]\theta[/tex] = 64°
- side opposite the angle = x
- hypotenuse = 30
[tex]\implies \sin(64\textdegree)=\dfrac{x}{30}[/tex]
[tex]\implies x=30\sin(64\textdegree)[/tex]
[tex]\implies x=27.0\textsf{ (nearest tenth)}[/tex]
