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

Answer:

$a=1.749$

Step-by-step explanation:

Recall Law of Sines

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

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"

$\frac{sin(35)^\circ}{a}=\frac{sin(139^\circ)}{2}\\ asin(139^\circ)=2sin(35^\circ)\\a=\frac{2sin(35^\circ)}{sin(139^\circ)}\\ a\approx1.749$