Question

Which trigonometric function would you use to solve the problem? If S=27° and TR=7 find TS (picture provided)

Answer 1

b. sin or csc

Explanation:

Remember that sine trigonometric function is the ratio of the opposite side of a right triangle to its hypotenuse; in other words:

`sin(\alpha )=(opposite-side)/(hypotenuse)`

Also, the cosecant is the inverse of sine, so:

`csc(\alpha )=(1)/(sin(\alpha) ) =(hypotenuse)/(opposite-side)`

Now, for our triangle, our angle is 27°, the longest side of it is TS, and the opposite side of our angle (27°) is TR; therefore,
`\alpha =27`,
`hypotenuse=TS`, and
`opposite-side=TR`.

Replacing values:

- Using the sine trigonometric function

`sin(\alpha )=(opposite-side)/(hypotenuse)`

`sin(27)=(TR)/(TS)`

`sin(27)=(TR)/(TS)`

`sin(27)=(7)/(TS)`

`TS=(7)/(sin(27))`

`TS=15.42`

- Using the cosecant trigonometric function

`csc(\alpha )=(hypotenuse)/(opposite-side)`

`csc(27)=(TS)/(TR)`

`csc(27)=(TS)/(7)`

`TS=7csc(27)`

`TS=15.42`

We can conclude that we can use either the sine trigonometric function or the cosecant trigonometric function to solve the problem.