Question

Triangle xyz is a right triangle with lengths shown what is the decimal value of sin z? Round the answer to the nearest thousandths.
If you could also show me how to solve these sorts of questions, I would love it!

Answer 1

A trick to solve these kind of problems would be...

SOHCAHTOA

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Aka

Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent

Then your answer to find Sin Z...
You're looking for an angle measurement so you're going to use an inverse operation.

You'd do...

Sin = 24/40

24/40 = .6

Then you'd use your inverse so...

Z°= Sin^-1(.6)

Z = 36.8698°

Rounding

Z = 36.870°

If you're using a scientific calculator. Make sure to put your calculator in degree mode to find the angle measurements and in radians to find missing side lengths.