Question

∆АВС АС=1. С=120° АВ-?​

Answer 1

Ответ:

ответ : 2

Объяснение:

воспользуемся теоремой косинусов

Answer 2

To find the length of side AB in triangle ABC when AC = 1 and ∠C = 120°, you can use the Law of Cosines. The Law of Cosines relates the lengths of the sides and the cosine of one of the angles in a triangle. Here's the formula:

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

Where:

• c is the length of side AC,
• a is the length of side AB (which we want to find),
• b is the length of side BC (which is unknown), and
• C is the angle between sides AC and BC, which is given as 120°.

Plugging in the values:

• c = 1
• C = 120°

The formula becomes:

1^2 = a^2 + b^2 - 2ab * cos(120°)

Now, calculate the cosine of 120°:

cos(120°) = -1/2

So, the equation becomes:

1 = a^2 + b^2 - 2ab * (-1/2)

Now, simplify:

1 = a^2 + b^2 + ab

We can't directly solve for both a and b with this equation because there are two variables and only one equation. However, we can express one variable in terms of the other. Let's solve for b in terms of a:

b = (1 - a^2) / (a + 1)

Now, we can substitute this expression for b into the original equation:

1 = a^2 + [(1 - a^2) / (a + 1)]^2 + a * [(1 - a^2) / (a + 1)]

Now, you can solve this equation for the value of a. Once you find the value of a, you can then use it to calculate the length of side AB (a). This is a quadratic equation, and you'll need to solve it for a numerically. The exact solution involves some algebraic manipulation and may be a bit complex, but it can be solved using numerical methods or a calculator.