we know that
The Cosecant is a trigonometric function that is the reciprocal of the sine
so
\(csc(x)=\frac{1}{sin(x)}\)
In this problem
Find the csc(B)
\(sin(B)=\frac{AC}{BC}\)
substitute the values
\(sin(B)=\frac{5}{6}\)
so
\(csc(B)=\frac{6}{5}\)
Find the csc(C)
\(sin(C)=\frac{AB}{BC}\)
substitute the values
\(sin(C)=\frac{4}{6}\)
Simplify
\(sin(C)=\frac{2}{3}\)
so
\(csc(C)=\frac{3}{2}\)
Statements
case A) csc right triangle B right triangle equals fraction \(3\) over \(2\)
The statement is false
Because, the value of csc(B) equals fraction \(6\) over \(5\)
case B) csc right triangle C right triangle equals fraction \(3\) over \(2\)
The statement is true
See the procedure
case C) csc right triangle B right triangle equals fraction \(6\) over \(5\)
The statement is true
See the procedure
case D) csc right triangle C right triangle equals fraction \(5\) over \(6\)
The statement is false
Because, Because, the value of csc(C) equals fraction \(3\) over \(2\)
