Answer :
Answer:
[tex]\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]
Step-by-step explanation:
The angle [tex]\theta_1[/tex] is located in Quadrant I and [tex]\cos(\theta_1)=\frac{3}{8}[/tex]
From Trigonometric ratio, In the First Quadrant
[tex]\cos \theta=\frac{Adjacent}{hypotenuse}[/tex]
Adjacent =3, Hypotenuse =8
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\8^2=Opposite^2+3^2\\Opposite^2=64-9=55\\Opposite=\sqrt{55}[/tex]
Therefore:
[tex]\sin(\theta_1)=\frac{Opposite}{Hypotenuse}\\\sin(\theta_1) =\frac{\sqrt{55} }{8}[/tex]