Consider this task and analyze the available data;
Since, according to the condition of the task, we know two angles and the side of the triangle, we can use the theorem of sines;
Recall and write this theorem for a given triangle;
The sides of a triangle are proportional to the sines of the opposite angles.
FB / sinD = BD / sinF = DF / sinB;
From this equality we take the following;
FB / sinD = BD / sinF;
Express the required side of BD;
BD = FB * sinF / sinD;
Let’s substitute the data;
BD = 4 * sin30 / sin45;
BD = 4 * 1/2 / √2 / 2;
BD = 4 / √2 ≈ 2.83.
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