Question

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

A. csc right triangle B right triangle equals fraction 3 over 2

B. csc right triangle C right triangle equals fraction 3 over 2

C. csc right triangle B right triangle equals fraction 6 over 5

D. csc right triangle C right triangle equals fraction 5 over 6

Answer 1

we know that

The Cosecant is a trigonometric function that is the reciprocal of the sine

so

`csc(x)=(1)/(sin(x))`

In this problem

Find the csc(B)

`sin(B)=(AC)/(BC)`

substitute the values

`sin(B)=(5)/(6)`

so

`csc(B)=(6)/(5)`

Find the csc(C)

`sin(C)=(AB)/(BC)`

substitute the values

`sin(C)=(4)/(6)`

Simplify

`sin(C)=(2)/(3)`

so

`csc(C)=(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`