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Scalene Triangle

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There is a scalene triangle with angles A, B, and C. Angle B is 145 degrees. Side length AB is 1017.5 cm long, and side length AC is 2035 cm long. Find angle C.

(Side AC is directly opposite of angle B)

Write your answer in scientific notation, Float 2 (For example $$2.09 \times 10^3$$)

So, the answer to this problem is $$1.67 \times 10^1$$ , but I don't know how to solve this problem and I need to come up with a reasoning. Can anyone help.?

Nov 24, 2018

#1
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From the information that you have given, it is angle A=16.67 degrees, NOT angle C!.
Calculation of the inner angles of the triangle using  Law of Cosines
A = b^2+c^2 - 2bc cos( A )
A = arccos(  a^2-b^2-c^2 }{ 2bc } ) = arccos(  1017.5^2-2035^2-1116.03^2 }{ 2 * 2035 * 1116.03 } ) = 16° 39'57"
Sides: a = 1,017.5 b = 2,035 c = 1,116.031

Area: T = 325,665.555
Perimeter: p = 4,168.531
Semiperimeter: s = 2,084.265

Angle  A = 16.666° = 16°39'57″

Angle  B = 145°
Angle  C = 18.334° = 18°20'3″

Nov 24, 2018
#2
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Using the Law of Sines

sin B            sin C

____    =    _____

AC             AB

sin 145           sin C

______   =    _______

2035             1017.15

sin C   =  (1017.5) * sin (145) / 2035

arcsin   [ (1017.5) * sin (145) / 2035 ] =  C = 16.67° ≈ [1.67 x 10^1 ] °   Nov 24, 2018