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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

Given the triangle below, which of the following is a correct statement? A. csc right-example-1

1 Answer

3 votes

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


User Tomblarom
by
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