Question

1)Дан треугольник ABC. Найдите величину угла С, если AC=AB=4, BC=4√3. и ещё один подобный номер: 2) Дан остроугольный треугольник ABC. Найдите величину угла B, если AC=7√6, BC=14, угол A=45°. Буду благодарна, если подробно распишите.

Answer 1

По теореме косинусов
АВ²=АС²+ВС²-2*АС*ВС*cosC
16=16+48-2*4*4√3*cosC
32√3cosC=48
CosC=48/32√3=√3/2
C=30град

по теор синусов
АС/sinB=BC/sinA
sinB=AC*sinA/BC=(7√6*√2/2)/14=√3/2
D=60 град

Answer 2

Task 1: Finding the angle C in triangle ABC

To find the angle C in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are given that AC = AB = 4 and BC = 4√3. Let's substitute these values into the equation and solve for angle C.

c^2 = a^2 + b^2 - 2ab * cos(C) (4√3)^2 = 4^2 + 4^2 - 2 * 4 * 4 * cos(C) 48 = 16 + 16 - 32 * cos(C) 48 = 32 - 32 * cos(C) 32 * cos(C) = 32 cos(C) = 1 C = arccos(1)

Using the inverse cosine function, we find that C = 0 degrees.

Therefore, the angle C in triangle ABC is 0 degrees.

Task 2: Finding the angle B in triangle ABC

To find the angle B in triangle ABC, we can use the Law of Sines. The Law of Sines states that in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In this case, we are given that AC = 7√6, BC = 14, and angle A = 45°. Let's substitute these values into the equation and solve for angle B.

sin(A) / a = sin(B) / b sin(45°) / 7√6 = sin(B) / 14 (1/√2) / 7√6 = sin(B) / 14 1 / (7√2 * √6) = sin(B) / 14 √6 / (7 * 2√2) = sin(B) / 14 √6 / (14√2) = sin(B) / 14 √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B) √6 / (2√2) = sin(B