Question

In ABC find a if b = 2, C = 6, and A=35°

Show work plzz!!!!

Answer 1

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 2

`a=1.749`

Explanation:

Recall Law of Sines

`(sin(A))/(a)=(sin(B))/(b)=(sin(C))/(c)`

Solve for angle B

`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`

Determine side "a" given angle B and side "b"

`(sin(35)^\circ)/(a)=(sin(139^\circ))/(2)\\ asin(139^\circ)=2sin(35^\circ)\\a=(2sin(35^\circ))/(sin(139^\circ))\\ a\approx1.749`