In ABC find a if b = 2, C = 6, and A=35°
Show work plzz!!!!
2 answers:
This problem cannot satisfy the triangle inequality. The triangle cannot be constructed and therefore solved.
a = 35
b = 2
c = 6
b+c ≤ a
2 + 6 ≤ 35
41 ≤ 35
The sum of the lengths of sides b, c must be greater than the length of the remaining side a.
Answer:
![a=1.749](https://tex.z-dn.net/?f=a%3D1.749)
Step-by-step explanation:
<u>Recall Law of Sines</u>
![\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28A%29%7D%7Ba%7D%3D%5Cfrac%7Bsin%28B%29%7D%7Bb%7D%3D%5Cfrac%7Bsin%28C%29%7D%7Bc%7D)
<u>Solve for angle B</u>
![A^\circ+B^\circ+C^\circ=180^\circ\\35^\circ+B^\circ+6^\circ=180^\circ\\41^\circ+B^\circ=180^\circ\\B^\circ=139^\circ](https://tex.z-dn.net/?f=A%5E%5Ccirc%2BB%5E%5Ccirc%2BC%5E%5Ccirc%3D180%5E%5Ccirc%5C%5C35%5E%5Ccirc%2BB%5E%5Ccirc%2B6%5E%5Ccirc%3D180%5E%5Ccirc%5C%5C41%5E%5Ccirc%2BB%5E%5Ccirc%3D180%5E%5Ccirc%5C%5CB%5E%5Ccirc%3D139%5E%5Ccirc)
<u>Determine side "a" given angle B and side "b"</u>
![\frac{sin(35)^\circ}{a}=\frac{sin(139^\circ)}{2}\\ asin(139^\circ)=2sin(35^\circ)\\a=\frac{2sin(35^\circ)}{sin(139^\circ)}\\ a\approx1.749](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%2835%29%5E%5Ccirc%7D%7Ba%7D%3D%5Cfrac%7Bsin%28139%5E%5Ccirc%29%7D%7B2%7D%5C%5C%20asin%28139%5E%5Ccirc%29%3D2sin%2835%5E%5Ccirc%29%5C%5Ca%3D%5Cfrac%7B2sin%2835%5E%5Ccirc%29%7D%7Bsin%28139%5E%5Ccirc%29%7D%5C%5C%20a%5Capprox1.749)
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