Question

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

Answer 1

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:

$sin(\alpha )=\frac{opposite-side}{hypotenuse}$

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

$csc(\alpha )=\frac{1}{sin(\alpha) } =\frac{hypotenuse}{opposite-side}$

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

$sin(\alpha )=\frac{opposite-side}{hypotenuse}$

$sin(27)=\frac{TR}{TS}$

$sin(27)=\frac{TR}{TS}$

$sin(27)=\frac{7}{TS}$

$TS=\frac{7}{sin(27)}$

$TS=15.42$

- Using the cosecant trigonometric function

$csc(\alpha )=\frac{hypotenuse}{opposite-side}$

$csc(27)=\frac{TS}{TR}$

$csc(27)=\frac{TS}{7}$

$TS=7csc(27)$

$TS=15.42$

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