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

Asked by wiki @ 16/11/2020 in Mathematics viewed by 277 People

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

Answered by wiki @ 16/11/2020

we know that

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

$csc(x)=\frac{1}{sin(x)}$

In this problem

Find the csc(B)

$sin(B)=\frac{AC}{BC}$

substitute the values

$sin(B)=\frac{5}{6}$

$csc(B)=\frac{6}{5}$

Find the csc(C)

$sin(C)=\frac{AB}{BC}$

substitute the values

$sin(C)=\frac{4}{6}$

Simplify

$sin(C)=\frac{2}{3}$

$csc(C)=\frac{3}{2}$

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 $2$

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