Answer:
b. sin or csc
Step-by-step explanation:
Remember that sine trigonometric function is the ratio of the opposite side of a right triangle to its hypotenuse; in other words:
[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]
Also, the cosecant is the inverse of sine, so:
[tex]csc(\alpha )=\frac{1}{sin(\alpha) } =\frac{hypotenuse}{opposite-side}[/tex]
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, [tex]\alpha =27[/tex], [tex]hypotenuse=TS[/tex], and [tex]opposite-side=TR[/tex].
Replacing values:
- Using the sine trigonometric function
[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]
[tex]sin(27)=\frac{TR}{TS}[/tex]
[tex]sin(27)=\frac{TR}{TS}[/tex]
[tex]sin(27)=\frac{7}{TS}[/tex]
[tex]TS=\frac{7}{sin(27)}[/tex]
[tex]TS=15.42[/tex]
- Using the cosecant trigonometric function
[tex]csc(\alpha )=\frac{hypotenuse}{opposite-side}[/tex]
[tex]csc(27)=\frac{TS}{TR}[/tex]
[tex]csc(27)=\frac{TS}{7}[/tex]
[tex]TS=7csc(27)[/tex]
[tex]TS=15.42[/tex]
We can conclude that we can use either the sine trigonometric function or the cosecant trigonometric function to solve the problem.
