Find side BD using trace data: Given triangle DBF, BF = 4 Angle F = 30 degrees Angle D = 45 degrees

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.