Answer: 55.5 (A.)
Step-by-step explanation:
Since angle A = 29 and angle B = 41, angle C must be equal to 110
180 = m<A + m<B + m<C
180 = 29 +41 + m<C
180 = 70 + m<C
110 = m<C
Therefore, side c must be the longest, side b must be the second longest, and side a must be the shortest.
Since side length a, angle A, and angle B are known, one can use the law of sines to solve for side b.
Law of Sines: sinA/a = sinB/b = sinC/c
sinA/a = sinB/b
sin29/41 = sin41/b
b(sin29/41) = sin41
b = 41(sin41)/(sin29)
b = 55.48
b = 55.5
4a-13=19 add 13 to both sides
4a=32 divide by 4 on both sides
a=8
(c/b) - x = 2d
(c/b) = 2d + x
c = b(2d + x)
c = 2db + bx
ac + bd = x
ac = x - bd
c = (x - bd) / a OR c = (x/a) - (bd/a)
