Mathematics
Therndon50:

In triangle LMN, LM = 6, MN = 9, and LN = 7. Find m∠M to the nearest tenth of a degree. A. 50.0 degrees B. 41.8 degrees C. 45.5 degrees D. 87.3 degrees

AZ:

|dw:1614795444333:dw|

AZ:

Do you know the law of cosine? @Therndon50

Therndon50:

a little

Therndon50:

@AZ

AZ:

So if know three sides, we can find the angle of one of them

AZ:

Take a look at the formula

AZ:

Do you think you can set up the formula to find the angle M for our question?

Therndon50:

Not really @AZ

Therndon50:

Thank you for the formulas @AZ

AZ:

You don't have to tag me each time :) I get a notification whenever you respond to the post!

AZ:

so if you look at the formulas, if we're trying to find an angle like M, then we use the formula that has the side opposite to it so in our case, we'll have (LN)^2 = (LM)^2 + (MN)^2 - 2*(LM)*(MN)*(cos M) and we already know from the question LN = 7 LM = 6 MN = 9

AZ:

Does that make sense? Can you plug in the numbers now

Therndon50:

Yes, I just can't figure out what cosine to use

AZ:

what do you mean? first let's simplify all the numbers and then we can solve for M once you get to cos M = some number we have to do the inverse of cos on your calculator, it can be written as cos^-1 or as arccos

AZ:

so cos M = some number then on your calculator arccos (some number) = the angle M

AZ:

so let's plug in your numbers, shall we? 7^2 = 6^2 + 9^2 - 2*(6)*(9)*(cos M) can you simplify it? what is 7^2 = 6^2 = 9^2 =

Therndon50:

I dont think I'm setting the equation right

Therndon50:

I got an answer of 59.1

AZ:

mhmm if you want, we can go through it step by step or if you show me your work, I can try to find out where you went wrong

Therndon50:

ok I tried it again, I got 50.1

Therndon50:

is that close?

AZ:

Now that is the correct answer!

Therndon50:

ok Thank you so much

AZ:

I guess in your answer choices, they somehow must have rounded off in one of the earlier calculations to end up with 50.0

AZ:

Of course! I'm glad you were able to solve it!!

TETSXPREME:

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