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olga55 [171]
3 years ago
5

Find m< x (Type the number answer)

Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

<em>x=74.73°</em>

Step-by-step explanation:

<u>Law of cosines</u>

In a general triangle, the law of cosines relates the lengths of the sides of the triangle to the cosine of one of its angles.

The law of cosine is expressed as:

\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos x

Where a and b are the lengths of two sides of the triangle, x is the angle contained between them, and c is the other side length.

If all side lengths are known, we can solve the above equation for the angle x:

\displaystyle x =\arccos \left({\frac {a^{2}+b^{2}-c^{2}}{2ab}}\right)

From the image, we must select a and b as the sides adjacent to angle x in any order. Thus a=17, b=22, c=24. Substituting:

\displaystyle x=\arccos \left({\frac {17^{2}+22^{2}-24^{2}}{2(17)(22)}}\right)

Operating:

\displaystyle x=\arccos \left({\frac {289+484-576}{748}}\right)

\displaystyle x=\arccos \left({\frac {197}{748}}\right)

Using a scientific calculator:

x=74.73°

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