Question

Find m< x (Type the number answer)

Answer 1

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:

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

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°