Question

Сторона треугольника равна 16 см ,а радиус окружности ,описанной около треугольника ,равен 8 корней из 2 .Чему равен угол треугольника ,противолежащий данной стороне ?

Answer 1

По теореме синусов: а/SinA=2R; 16/SinA=2*8√2; SinA=16/16*√2=1/√2=√2/√2*√2 =√2/√4=√2/2; A=45°; или А=135°; так как Sin135°=Sin(180-45)=Sin45°=√2/2; треугольник может быть остроугольным или тупоугольным. ответ: 45; 135

Answer 2

Given Information

We are given that one side of a triangle is 16 cm long and the radius of the circumcircle of the triangle is equal to 8√2.

Finding the Angle Opposite the Given Side

To find the angle opposite the given side, we can use the law of sines. The law of sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Let's denote the given side as a and the angle opposite it as A. The circumradius of the triangle is denoted as R.

According to the law of sines, we have the following relationship:

a / sin(A) = 2R

We are given that a = 16 cm and R = 8√2. Substituting these values into the equation, we can solve for sin(A).

16 / sin(A) = 2 * 8√2

Simplifying the equation, we get:

sin(A) = 16 / (2 * 8√2) = 1 / (2√2)

To find the value of A, we can take the inverse sine (arcsine) of 1 / (2√2).

A = arcsin(1 / (2√2))

Using a calculator, we can find the approximate value of A.

A ≈ 26.565 degrees.

Therefore, the angle of the triangle opposite the given side is approximately 26.565 degrees.