Question

What is the value of csc A in the triangle below

Answer 1

csc = 1/sin

sin A = 16/(sqrt(9^2 + 16^2))

sin A = 16/sqrt(337)

csc A = sqrt(337)/16

B

Answer 2

Step 1

Find the length of AC

In the right triangle ABC

Applying the Pythagoras Theorem

`AC^(2)=AB^(2)+BC^(2)`

In this problem we have

`AB=9\ units\\BC=16\ units`

Substitute

`AC^(2)=9^(2)+16^(2)`

`AC^(2)=337`

`AC=√(337)\ units`

Step 2

Find the csc(A)

we know that

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

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

so

`csc(A)=(AC)/(BC)`

substitute

`csc(A)=(√(337))/(16)`

therefore

the answer is

`csc(A)=(√(337))/(16)`