Thursday 12 December 2013

`a = 75.4, b = 52, c = 52` Use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Given: `a=75.4, b=52, c=52`


``


`cos(A)={b^2+c^2-a^2]/(2bc)`


` ` `cos(A)=[52^2+52^2-75^2]/(2*52*52)`


`cos(A)=-.04012`


`A=arccos(-.04012)`


`A=92.30^@`



`cos(B)=(a^2+c^2-b^2)/(2ac)`


` `


`cos(B)=[75^2+52^2-52^2]/(2*75*52)`


`cos(B)=.7211`


`B=arccos(.7211)`


`B=43.85^@`



`C=180-92.30-43.85`


`C=43.85^@`



Given: `a=75.4, b=52, c=52`


``


`cos(A)={b^2+c^2-a^2]/(2bc)`


` ` `cos(A)=[52^2+52^2-75^2]/(2*52*52)`


`cos(A)=-.04012`


`A=arccos(-.04012)`


`A=92.30^@`



`cos(B)=(a^2+c^2-b^2)/(2ac)`


` `


`cos(B)=[75^2+52^2-52^2]/(2*75*52)`


`cos(B)=.7211`


`B=arccos(.7211)`


`B=43.85^@`



`C=180-92.30-43.85`


`C=43.85^@`



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