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In triangle ABC, side a=, angle A=° and angle B=°. Find the length of side b.

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You have had three attempts at answering this question, so here is the solution:

This is a triangle, so we can use sin(B) to find b directly we apply the Sine Rule:

sin B = b a b = a sin B b = ia × sin iB = fAns \begin{eqnarray*} \\sin(B)&=&\frac{b}{a}\\ b&=&a\sin(B)\\ &=&\qv{ia}\times\sin(\qv{iB}) &=&\qv{fAns} \end{eqnarray*} a sin A = b sin B ia sin iA = b sin iB b = ia × sin iB sin iA = ia × sinB sinA = fAns \begin{eqnarray*} \frac{a}{\sin(A)}&=&\frac{b}{\sin(B)}\\ \frac{\qv{ia}}{\sin(\qv{iA})}&=&\frac{b}{\sin(\qv{iB})} b&=&\frac{A\times\sin(B)}{\sin(A)}\\ &=&\frac{\qv{ia}\times\sin(\qv{iB})}{\sin(\qv{iA})}\\ &=&\qv{fAns} \end{eqnarray*}

So the expected answer is .

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