SOLUTION: I have a triangle with two equal sides 276". Angle between the two equal sides is 16.3636364. What is the length of the other side of the triangle

Question 854203: I have a triangle with two equal sides 276". Angle between the two equal sides is 16.3636364.
What is the length of the other side of the triangle
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the other 2 angles of the triangle will be equal to (180 - 16.3636364)/2.

this makes each of them equal to 81.8181818.

you can use the law of sines to find the third side.

the law of sines says that a/sinA = b/sinB = c/sinC

let A = the angle that is 16.3636364 degrees and let a = x because that's the side opposite that angle that we don't know about.

let B = one of the angles that is 81.8181818 degrees and let b = 276 because that's the side opposite that angle that we do know about because it was given.

the part of the law of sines formula that we are interested in is:

a/sinA = b/sinB

that becomes x /sin(16.3636364) = 276 / sin(81.8181818)

multiply both sides of this formula by sin(16.3636364) and you get:

x = 276 * sin(16.3636364) / sin(818181818) which gets you x = 78.5577909 inches.

you can confirm this is true by seeing that the ratio based on the law of sines is true.

78.5577909 / sin(16.3636364) is equal to 278.8381705.

276 / sin(81.8181818) is equal to 278.8381705.

the ratios are the same so the solution is good.

you could also have solved this using the law of cosines as follows:

the formula to use is c^2 = a^2 + b^2 - 2*a*b*cosC.

let C be the angle that you know about.
c is the side opposite this angle.
a and b are each 276 inches.
these are the sides that are opposite the other 2 angles that we don't know about and don't need to know about if we are using the law of cosines formula.

the law of cosines formula becomes:
c^2 = 276^2 + 276^2 - 2*276*276*cos(16.3636364).
solve this to get c^2 = 6171.326511
take the square root of both sides to get:
x = 78.5577909

you get the same answer either way.
that's good.

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