Question

Given the triangle below, which of the following is a correct statement?

Answer 1

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 $2$