Question

стороны треугольника равны 7 37 40 найдите угол противолежащий средней стороне треугольника

Answer 1

 

средняя сторона  37

угол противолежащий средней стороне треугольника  <A

теорема косинусов

37^2 = 7^2 +40^2 - 2*7*40 *cos<A

cos<A  = (37^2 - (7^2 +40^2 )) /  (-560) = 1/ 2

cos<A  = 1 / 2 <-----это  косинус  60 град

<A =60

ОТВЕТ 60 град

Answer 2

Finding the Angle Opposite the Middle Side of a Triangle

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

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

In this case, we are given that the sides of the triangle are 7, 37, and 40. We want to find the angle opposite the side of length 37.

Let's substitute the given values into the Law of Cosines equation:

37^2 = 7^2 + 40^2 - 2 * 7 * 40 * cos(C)

Simplifying the equation:

1369 = 49 + 1600 - 560 * cos(C)

Rearranging the equation:

560 * cos(C) = 1369 - 49 - 1600

560 * cos(C) = -280

cos(C) = -280 / 560

cos(C) = -0.5

To find the angle C, we can take the inverse cosine (also known as arccos) of -0.5:

C = arccos(-0.5)

Using a calculator, we find that C is approximately 120 degrees.

Therefore, the angle opposite the middle side of the triangle is approximately 120 degrees.