In triangle ABC, b = 600, ∠B = 11°, and ∠C = 75°. Find a.1151,1853,0373,137

Answer:a = 3,137Step-by-step explanation:We have to use the sin rule to solve. THis gives ratios of side and opposite side's angle's sin.Sin rule is:[tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex]First, we know there are 180 degrees in 3 angles of a triangle, so lets find ∠A:∠A + ∠B + ∠C = 180∠A + 11 + 75 = 180∠A + 86 = 180∠A = 180 - 86∠A = 94Now since we know the angle B and side b pair, we can relate with a and write the sin rule as:[tex]\frac{a}{SinA}=\frac{b}{SinB}\\\frac{a}{Sin94}=\frac{600}{Sin11}[/tex]Now we cross multiply and solve for side a:[tex]\frac{a}{Sin94}=\frac{600}{Sin11}\\aSin11=600Sin94\\a=\frac{600Sin94}{Sin11}\\a=3137[/tex]So last answer choice is right, a = 3137