Answer:
x = 155 cm
Step-by-step explanation:
The Law of Cosines
It relates the length of the sides of a triangle with one of its internal angles.
Let x,y, and z be the length of the sides of a given triangle, and X the included angle between sides y and z, then the following relation applies:
[tex]x^2=y^2+z^2-2yz\cos X[/tex]
It's given: y=75 cm, z=83 cm, and [tex]m\angle X=157[/tex] °
. Applying the formula:
[tex]x^2=75^2+83^2-2*75*83\cos 157^\circ[/tex]
Calculating:
[tex]x^2=5625+6889-12450(-0.9205)[/tex]
[tex]x^2=23974.225[/tex]
[tex]x=\sqrt{23974.225}[/tex]
x = 155 cm
