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 Log in to Reply

Answer:x = 155 cmStep-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