In △ ABC, if AB = 3, a = 45 ° and C = 75 °, then BC = () A. 3−3B. 2C. 2D. 3+3

In △ ABC, if AB = 3, a = 45 ° and C = 75 °, then BC = () A. 3−3B. 2C. 2D. 3+3

∵ AB = 3, a = 45 °, C = 75 ° according to the sine theorem: Asina = csinc, {bcsin45 ° = absin75 ° = 36 + 24, ∵ BC = 3 − 3

Angle a = 45 degrees, angle B = 60 degrees, angle c = 75 degrees, AC = 2
What's that check sign?

According to sine theorem: sin45 ° / BC = sin60 ° / 2BC = (2 radical 6) / 3 triangle ABC area = (BC * acsin75 °) / 2sin75 ° = sin (30 ° + 45 °) = sin30 ° cos45 ° + cos30 ° sin45 ° = (√ 6 + √ 2) / 4 so: triangle ABC area = (2 radical 6) / 3 * 2 * (√ 6 + √ 2) / 8 = (3 + radical 3) / 3

In the triangle ABC, we know the edge BC = 2, the angle B = 60 degrees, and the angle c = 75 degrees. (1) find the angle a; (2) find the length of the edge AC

180-60-75 = 45 degrees;
2. Make CD perpendicular to AB and D, because angle a = 45 degrees, ADC is isosceles right angle, ad = DC = root 3
So AC = root 6

As shown in the figure, in known triangle ABC, angle B = 45 degrees, angle BAC = 75 degrees, and AC = 4, find AB and BC

Pass a as ad ⊥ BC and pass BC to point D
Because ∠ B = 45
So, bad = 45
Because ∠ BAC = 75
Therefore, CAD = 75-45 = 30
In ACD, CD = AC / 2 = 2, ad = 2 √ 3
So in the isosceles right triangle abd, BD = ad = 2 √ 3
According to Pythagorean theorem, ab = 2 √ 6
So AB = 2 √ 6, BC = BD + CD = 2 √ 3 + 2