Respuesta :

19allenethm

Firstly, we can look at our givens,

a = 17

b = 22

c = 30

And we are looking for m∠A

[tex]a^2=b^2 +c^2 -2bc (cosA)[/tex] Is the Law of Cosines. Now we can solve for our unknown, m∠A. This will give us

[tex]A = cos^{-1} (\frac{-a^2+b^2+c^2}{2bc})[/tex]

Now we can substitute in our given variables.

[tex]A= cos^{-1} (\frac{-(17^2)+27^2+30^2}{2(27)(30)} )[/tex]

Then we can plug this into our calculator which will give us

34.19185257 degrees

Now we just have to round to the nearest tenth

This means that the answer is 34.2 degrees

akposevictor

Using the Law of Cosines, the missing angle, m∠A = 34.0°

What is the Law of Cosines?

The Law of Cosines is given by the formula, a² = b² + c² - 2bc(Cos A)

  • Given:

a = 17

b = 22

c = 30

  • Required:

Find m∠A

Apply the law of Cosines formula, plug in the values:

17² = 22² + 30² - 2(22)(30)(Cos A)

289 = 1,384 - 1,320(Cos A)

289 - 1,384 =  -1,320(Cos A)

-1,095 = -1,320(Cos A)

  • Divide both sides by -1,320

0.8295 = Cos A

[tex]A = cos^{-1}(0.8295)\\A = 34.0[/tex]

Therefore, using the Law of Cosines, the missing angle, m∠A = 34.0°

Learn more about Law of Cosines on:

https://brainly.com/question/7872492

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