Please help with this: In triangle XYZ, side y is 8cm, side z is 5cm, and the measure of angle Y is 75 deg; find the length of side x
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Dr.Peterson
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You've stated the Law of Sines; now apply it in the only way possible. It won't take you immediately to the goal, but you'll be closer to it.
When you show your attempt (as we ask that you do in order to get help), there may be more to talk about.
The Highlander
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Referring to your (modified) picture, below, (qv)...
In the circled section there is only one thing you don't know, so you can easily find it.
Remember: \(\displaystyle \boxed{\frac{a}{b}=\frac{c}{d}\implies d=\frac{c\times b}{a}}\)
If you know two of the angles in a triangle, then third is easily found and, once you know the measure of \(\displaystyle \color{blue}\angle YXZ\) then the only thing left to find is "x"
Please now come back and show us your working and result, thank you.
Hope that helps.
You can also use the law of cosines (judiciously) and solve it.
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Dr.Peterson
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This is the second in a couple days, using an old account in the same way (to get past moderation). I reported it as such this morning.