Question

Знайдіть довжину сторони BC трикутника ABC, якщо AC=4√2 см; ∠A=30°; ∠B=45°;

Answer 1

За теоремою синусів a/sin a=b/sinb

Answer 2

I can help you with your math problem. Here is a detailed solution:

To find the length of BC, we can use the law of sines, which states that $$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$$ where A, B, and C are the angles of the triangle and a, b, and c are the opposite sides.

We know that AC = 4√2 cm, ∠A = 30°, and ∠B = 45°. We can find ∠C by using the fact that the sum of the angles of a triangle is 180°. Therefore, ∠C = 180° - 30° - 45° = 105°.

Now we can plug in the known values into the law of sines and solve for BC:

$$\frac{\sin 30°}{4\sqrt{2}}=\frac{\sin 45°}{BC}=\frac{\sin 105°}{AB}$$

$$BC=\frac{4\sqrt{2}\sin 45°}{\sin 30°}=\frac{4\sqrt{2}\cdot \frac{\sqrt{2}}{2}}{\frac{1}{2}}=8$$

Therefore, the length of BC is 8 cm.