Answer:
x=74.73°
Step-by-step explanation:
Law of cosines
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:
[tex]\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos x[/tex]
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:
[tex]\displaystyle x =\arccos \left({\frac {a^{2}+b^{2}-c^{2}}{2ab}}\right)[/tex]
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:
[tex]\displaystyle x=\arccos \left({\frac {17^{2}+22^{2}-24^{2}}{2(17)(22)}}\right)[/tex]
Operating:
[tex]\displaystyle x=\arccos \left({\frac {289+484-576}{748}}\right)[/tex]
[tex]\displaystyle x=\arccos \left({\frac {197}{748}}\right)[/tex]
Using a scientific calculator:
x=74.73°
