The angle X of the given triangle is equal to 83.0°.
Law of Cosines
This law is represented by the equation: C²=A²+B²-2ABcosθ, where: A,B and C are the sides of a triangle and θ=angle.
For solving this question, you should apply the Law of Cosines, where:
A=8ft
B=16ft
C=17 ft
θ=X
[tex]C^2=A^2+B^2-2*A*B*cos\theta \\ \\ 17^2=8^2+16^2-2*8*16*cosX\\ \\ 289=64+256-256*cosX\\ \\ 256cosX=256+64-289\\ \\ 256cosX=31\\ \\ cosX=\frac{31}{256}[/tex]
Therefore, [tex]arccos(\frac{31}{256} )=83.0^{\circ \:}[/tex].
Read more about the Law of Cosines here:
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