Question

Знайдіть невідомі сторони та кути трикутника ABC , якщо AB=6,AC=10,кут A =110

Answer 1

По теореме косинусов
ВС^2=6^2+10^2-2*6*10cos110
BC^2=36+100-120*(-cos70)
BC^2=136+120cos70
BC=coren(136+120cos70) ответ странный! ??

Answer 2

Finding the Unknown Sides and Angles of Triangle ABC

To find the unknown sides and angles of triangle ABC, we are given the following information: - AB = 6 - AC = 10 - Angle A = 110 degrees

Let's start by finding the unknown side BC.

Using the Law of Cosines, we can find the length of side BC. 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 our case, side a is AB, side b is AC, and angle C is angle A.

Plugging in the values, we have: BC^2 = AB^2 + AC^2 - 2 * AB * AC * cos(A)

Substituting the given values: BC^2 = 6^2 + 10^2 - 2 * 6 * 10 * cos(110)

Calculating the expression: BC^2 = 36 + 100 - 120 * cos(110)

Using a calculator, we can find the value of BC^2 to be approximately 244.4.

Taking the square root of both sides, we find: BC ≈ √244.4

Calculating the square root, we get: BC ≈ 15.63

So, the length of side BC is approximately 15.63.

Now, let's find the remaining angles of triangle ABC.

We know that the sum of the angles in a triangle is always 180 degrees. Since we already know angle A, we can find angles B and C by subtracting angle A from 180 and dividing the result by 2.

Angle B = (180 - Angle A) / 2 Angle B = (180 - 110) / 2 Angle B = 70 / 2 Angle B = 35 degrees

Angle C = (180 - Angle A) / 2 Angle C = (180 - 110) / 2 Angle C = 70 / 2 Angle C = 35 degrees

Therefore, the unknown angles of triangle ABC are: Angle B ≈ 35 degrees Angle C ≈ 35 degrees

To summarize: - Side BC ≈ 15.63 - Angle B ≈ 35 degrees - Angle C ≈ 35 degrees

Please note that these calculations are approximate due to rounding.