Answer:
[tex]a=56.4\degree[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be an acute angle.
To solve: [tex]\sin(a)=0.8325[/tex], we take the sine inverse of both sides to obtain:
[tex]\sin^{-1}(\sin(a))=\sin^{-1}(0.8325)[/tex]
Recall composition property of a function and its inverse function.
[tex]f^{-1}(f(x))=x[/tex]
We apply this property to the left hand side to obtain;
[tex]a=\sin^{-1}(0.8325)[/tex]
We now use our scientific calculator to obtain;
[tex]a=56.3564115\degree[/tex]
We round to the nearest tenth to obtain;
[tex]a=56.4\degree[/tex]
