The value of c is 4 feet for the given triangle it is obtained by law of cosines formula.
Step-by-step explanation:
The given is,
Triangular diagram with side dimensions
Step:1
Law of Cosines formula is,
[tex]c^{2}= a^{2}+b^{2} - 2ab cos C[/tex].......................(1)
From the given diagram,
a = 8 feet
b = 7 feet
Angle, C = 32°
Substitute the values then equation (1) becomes,
[tex]c^{2} =8^{2} +7^{2} -2(8)(7) cos 32[/tex]
[tex]= 64+49-2(56)cos32[/tex]
[tex]=113-(112)(cos 32)[/tex]
Substitute the value of cos 32°
[tex]=113-(112)(0.848)[/tex] (∵ [tex]cos32=0.848[/tex] )
[tex]= 113-(94.98)[/tex]
[tex]c^{2} =18.0186[/tex]
Take square root on both sides the above equation becomes,
[tex]c=\sqrt{18.0186}[/tex]
[tex]=4.244[/tex]
c ≅ 4 feet
Result:
The value of c is 4 feet for the given triangle it is obtained by law of cosines formula.
Answer:
4.2
Step-by-step explanation:
c=√a2+b2﹣2abcosγ = √72+82﹣2·7·8·cos(32°) ≈ 4.24483
Hope this helps :)