Question

Using the value from the previous question, find the measure of angle Y and the length of side y.

Answer 1

X=89.9

Answer 2

Y=21.92 so all i need is the y but i dont know what to use to solve it

Answer 3

@tomhue maybe you can help me solve this

Answer 4

You can use the Law of Cosines here. The formula is (lowercase = side, capital = angle):
\[c^2 = a^2 + b^2 - 2ab * \cos C\]
You can arbitrarily assign the a, b, and c labels to sides just as long as you use the angle opposite side c in the equation.

Answer 5

can this be set up with the law of sines as well?

Answer 6

Oh, yes. I forgot about that one. I just saw 3 sides and 1 angle and thought law of cosines. But yes, you can use the law of sines just the same.

If it's for homework, it probably expects you to use the law/formula you learned in the lesson. If you just learned law of sines, it probably wants law of sines. If you just learned law of cosines, it probably wants law of cosines. If you learned both in one lesson, then it doesn't matter; law of sines is probably the easier route.

Answer 7

it wants me to use law of sines, but im so confused with trig and i dont know how to set it up to solve it, however i am fixing to need to know the law of cosines. can you help me solve it in both laws?

Answer 8

Sure thing!

First, let's do the law of sines method.
\[\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}\]
The third one doesn't matter. It really just means put the sine of the angle over the opposite side, and it equals all the others set up like that.
Let's fix up the diagram so it only shows what we want to use.

This means:
\[\frac{\sin 67.38}{24} = \frac{\sin 21.92}{y}\]
We can use cross products to find y*sin(67.38)=24*sin(21.92). If you plug those sine values into a calculator, you get: -0.99y=24*0.07
You can simplify and solve for y.

-0.99y=1.68
y=-1.7

Answer 9

that's actually kinda cool

Answer 10

Now, law of cosines.
\[c^2=a^2+b^2-2ab*\cos C\]
Let's fix up the diagram again.

Now, we're just going to plug some values in.
\[y^2=26^2+24^2-2(26)(24)*\cos(21.92)\]
This can be simplified down to:
\[y^2=676+576+(-1248\cos(21.92))=1252+(1244.84)=3396.84\]
...I screwed up somewhere, I'm so sorry. I just realized that my answer was negative for the law of sines, too. I don't know what went wrong where. The formulas are correct, but I guess somehow my work is not. It's up to you :(

Answer 11

ok well just the same thank you so much for showing me how to do it and puting up the different formulas. i do apriciate it :)