Question

A=8 cm β=45° γ=60° α=?; b=?; c=?

Answer 1

Відповідь:

Ответ: α = 75°, b = 4√2, c = 4√3.

Покрокове пояснення:

sin α / a = sin β / b = sin γ / c

Также в треугольнике сумма углов равна 180°. Используя эти факты, можно решить задачу.

Сначала найдем угол α:

180 - 45 - 60 = 75°

Теперь найдем b:

b = a * sin β / sin α = 8 * sin 45° / sin 75° = 8 * √2 / √6 = 4√6 / √6 = 4√2

Наконец, найдем c:

c = a * sin γ / sin α = 8 * sin 60° / sin 75° = 8 * √3 / √6 = 4√3

Answer 2

To find the missing values α, b, and c, we'll use the properties of a triangle and the given information.

Given: A = 8 cm β = 45° γ = 60°

We know that the sum of angles in a triangle is always 180°. So, we can find α by subtracting the sum of β and γ from 180°:

α = 180° - β - γ α = 180° - 45° - 60° α = 75°

Now, we can use the Law of Sines to find the values of b and c. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In equation form:

a/sin(α) = b/sin(β) = c/sin(γ)

We are given the value of A (opposite to angle α) as 8 cm. Using the Law of Sines, we can find the values of b and c.

b/sin(β) = A/sin(α) b/sin(45°) = 8 cm/sin(75°)

Let's calculate b:

b = (8 cm * sin(45°)) / sin(75°) b ≈ 8 cm * 0.7071 / 0.9659 b ≈ 5.8 cm

Similarly, using the Law of Sines, we can find the value of c:

c/sin(γ) = A/sin(α) c/sin(60°) = 8 cm/sin(75°)

Let's calculate c:

c = (8 cm * sin(60°)) / sin(75°) c ≈ 8 cm * 0.8660 / 0.9659 c ≈ 7.2 cm

Therefore, the missing values are: α ≈ 75° b ≈ 5.8 cm c ≈ 7.2 cm