Question

В треугольнике abc ab=8cm, bc=15cm, ac=17cm. найдите противолежащий угол? срочно пожалуйста!

Answer 1

По теореме Пифагора доказываем , что треугольник ABC прямоугольный: AC^2=AB^2+BC^2 AC^2=289 ^2
AC=17, значит угол, противолежащий большей стороне треугольника  равен 90 градусов

Answer 2

Finding the Angle in a Triangle

To find the angle opposite side AB 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 have side AB = 8 cm, side BC = 15 cm, and side AC = 17 cm. Let's denote the angle opposite side AB as angle C.

Using the Law of Cosines, we can substitute the values into the equation and solve for cos(C):

8^2 = 15^2 + 17^2 - 2 * 15 * 17 * cos(C)

Simplifying the equation:

64 = 225 + 289 - 510 * cos(C) 64 = 514 - 510 * cos(C) 510 * cos(C) = 514 - 64 510 * cos(C) = 450 cos(C) = 450 / 510 cos(C) ≈ 0.8824

Now, we can find the angle C by taking the inverse cosine (cos^-1) of 0.8824:

C ≈ cos^-1(0.8824) C ≈ 29.7 degrees

Therefore, the angle opposite side AB in triangle ABC is approximately 29.7 degrees.