Zack, Rachel, and Maddie are unraveling a huge ball of yarn to see how long it is. As they move away from each other, they form a triangle. The distance from Zack to Rachel is 3 meters. The distance from Rachel to Maddie is 2.5 meters. The distance from Maddie to Zack is 4 meters. Find the measures of the three angles in the triangle.

Question

anonymous · Answer

looks like a law of cosines problem to me

warpedkitten · Answer

It is, but I'm not understanding it. I've done similar problems and it seems like every time I try, I don't get any of the answer choices.

anonymous · Answer

lets agree on this labelling, i will let you fill in the names etc

anonymous · Answer

|dw:1433387769343:dw|

anonymous · Answer

B is opposite the largest side, so it is the largest angle, we can find that first

anonymous · Answer

$$b^2=a^2+c^2-2ac\cos(B)$$ but we want the angle so 
$$\cos(B)=\frac{a^2+c^2-b^2}{2ac}$$

anonymous · Answer

filling in the numbers we get 
$$\cos(B)=\frac{3^2+2.5^2-4^2}{2\times 3\times 2.5}$$

anonymous · Answer

take the arccosine to find B

princeevee · Answer

satellite can you help me?

anonymous · Answer

i must have made some mistake here

anonymous · Answer

oh, no i didn't here use the calculator http://www.wolframalpha.com/input/?i=arccos%28%283^2%2B2.5^2-4^2%29%2F%282*3*2.5%29%29

anonymous · Answer

looks like the largest angle is $92.87^\circ$
find the next one of your choice using the law of sines

warpedkitten · Answer

I've got it now, thank you!