Answer:
57.8 degrees and 122.2 degrees (to one decimal place)
Step-by-step explanation:
Since there are two pairs of angle/side involved, we can use the sine rule.
sin(A)/a = sin(B)/b
where
A = angle x
a = 11cm
B = 38 degrees
b = 8 cm
substitute in the sine rule equation,
sin(A) = sin(x) = sin(38)/8 * 11 = 0.61566 * 11/8 = 0.84653
Now there are two solutions for x where sin(x) = 0.84653, they are supplement angles, namely 57.8367 degrees and 122.1633 degrees.
The reason for the two solutions is because the 8cm side can swing in two positions, one that makes x acute, and the other one obtuse.
