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lakkis [162]
2 years ago
8

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

Mathematics
1 answer:
Kay [80]2 years ago
8 0

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.

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