Question

АВ=437м АС=270м <АВС=114’ найти ВС, площадь

Answer 1

Рисунок только неверний

Answer 2

To find the length of side BC (VS in the original notation) and the area of triangle ABC, we can use trigonometry and the formula for the area of a triangle.

Given: AB = 437m AC = 270m ∠ABC = 114 degrees

Step 1: Find the length of side BC (VS).

We can use the law of cosines to find the length of BC: Cosine law: c^2 = a^2 + b^2 - 2ab * cos(C)

Let a = AB = 437m Let b = AC = 270m Let C = ∠ABC = 114 degrees

VS^2 = AB^2 + AC^2 - 2 * AB * AC * cos(∠ABC) VS^2 = 437^2 + 270^2 - 2 * 437 * 270 * cos(114 degrees)

Now, calculate VS:

VS^2 = 190969 + 72900 - 2 * 437 * 270 * (-0.34202014332) VS^2 = 190969 + 72900 + 198129.92419 VS^2 = 462998.92419

VS ≈ √462998.92419 VS ≈ 680.306 meters

Step 2: Calculate the area of triangle ABC.

The area of a triangle can be calculated using the formula: Area = (1/2) * base * height

We can use side BC (VS) as the base and drop a perpendicular from A to BC to find the height.

Let h = height of triangle ABC from point A to side BC.

Using trigonometry, we can find that: sin(∠ABC) = h / AB h = AB * sin(∠ABC)

Now, calculate the height:

h = 437m * sin(114 degrees) h ≈ 437m * 0.92718385457 h ≈ 405.006 meters

Now, calculate the area:

Area = (1/2) * base * height Area = (1/2) * 680.306m * 405.006m Area ≈ 138048.49 square meters

So, the length of side BC (VS) is approximately 680.306 meters, and the area of triangle ABC is approximately 138048.49 square meters.