We can use the sine rule for this problem.
Sine rule formula is:
[tex] \frac{a}{Sin A} =\frac{b}{Sin B} =\frac{c}{Sin C} [/tex]
Where a (side BC), b (side AC) and c (side AB) are the opposite sides of the angle A, B and C repectively.
According to the given figure,
B= 79°, C = 30° and AB= c =11 and we need to find side BC= a.
Hence, first step is to find the angle A.
Sum of all angles of a triangle is 180°.
So, ∠A +∠B + ∠C = 180.
∠A + 79 + 30 = 180
∠A + 109 = 180
∠A = 180 - 109
∠A = 71°.
So, let's use the formula:
[tex] \frac{a}{Sin A} =\frac{c}{Sin C} [/tex]
[tex] \frac{a}{Sin 71} =\frac{11}{Sin 30} [/tex]
[tex] \frac{a}{0.9455} =\frac{11}{0.5} [/tex]
[tex] \frac{a}{0.9455} =22 [/tex]
[tex] \frac{a}{0.9455}*0.9455 =22*0.9455 [/tex]
So, a = 20.801
Therefor BC is 20.8 ( Rounded to nearest tenth).
"Hope this helps!!"
