Answer:
[tex]p\approx 4.52\text{ cm}[/tex]
Step-by-step explanation:
We can solve for p using the trigonometric ratio sine (or cosine):
[tex]\sin(\theta)=\dfrac{\rm opposite}{\rm hypotenuse}[/tex]
Plugging in the given values, we get:
[tex]\sin(65\°) = \dfrac{4.1}{p}[/tex]
↓ taking the reciprocal of both sides
[tex]\dfrac{1}{\sin(65\°)} = \dfrac{p}{4.1}[/tex]
↓ multiplying both sides by 4.1
[tex]\dfrac{4.1}{\sin(65\°)}=p[/tex]
↓ evaluating using a calculator
[tex]\boxed{p\approx 4.52\text{ cm}}[/tex]