Given that the length of the hypotenuse is 8 and the angle is 42°
The length of the one leg of the triangle is x.
We need to determine the value of x.
Value of x:
The value of x can be determined using the trigonometric ratio.
Thus, we have;
[tex]sin \ \theta=\frac{opp}{hyp}[/tex]
Substituting the values, we get;
[tex]sin \ 42^{\circ}=\frac{x}{8}[/tex]
Multiplying both sides of the equation by 8, we get;
[tex]sin \ 42^{\circ}\times8=x[/tex]
Simplifying, we get;
[tex]0.669 \times 8=x[/tex]
[tex]5.352\approx x[/tex]
Therefore, the value of x is 5.35(app.)
Hence, Option A is the correct answer.
