A triangle has sides A, B, and C. The angle between sides A and B is (3pi)/4. If side C has a length of 8 and the angle between sides B and C is pi/12, what are the lengths of sides A and B?

1 Answer
SCooke
Mar 18, 2018

A = 2.93
B = 5.66

Explanation:

Given two angles, the third one in a triangle is fixed. In this case it is 2pi/12. The shortest side length will be opposite the smallest angle, which is pi/12 in this case. We know that the side of length 8 is opposite the 9pi/12 corner.

We now have three angles and a side, and can calculate the other sides using the Law of Sines, and then calculate the height for the area.
https://www.varsitytutors.com/hotmath/hotmath_help/topics/law-of-sines

https://www.mathsisfun.com/algebra/trig-solving-asa-triangles.html

a/(sin(pi/12)) = c/sin C = 8/(sin(9pi/12))
b/(sin(2pi/12)) = c/sin C = 8/(sin(9pi/12))

a xx (sin(9pi/12)) = 8 xx (sin(pi/12))

b xx (sin(9pi/12)) = 8 xx (sin(2pi/12))

a xx 0.707 = 8 xx 0.259 ; a = 2.93
b xx 0.707 = 8 xx 0.50 ; b = 5.66

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