Question

Угол А=30° угол В=120°угол С=30° АС=√2Найти Рabc

Answer 1

Т.к. два угла в треуг. АВС равны, то он равнобедренный , стороны ВС и ВА равны между собой, пусть, например по х, по теореме косинусов найдем АС²=2х²-2х²*cos120°=2х²-2х²*(-0,5)=2

3х²=2, х=√(2/3)=√6/3/см/, тогда периметр равен

√2+√6/3+√6/3=√2+2√6/3/см/

Answer 2

To find the value of angle C and the measure of side BC (denoted as 'Рabc'), we can use the properties of a triangle.

Let's start by finding angle C: Since the sum of the angles in a triangle is always 180°, we can use the equation:

Angle A + Angle B + Angle C = 180°

Substitute the given values:

30° + 120° + Angle C = 180°

Now, solve for Angle C:

Angle C = 180° - 30° - 120° Angle C = 30°

Now that we have the value of angle C, let's use the law of sines to find the measure of side BC:

The law of sines states:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the sides of the triangle, and A, B, and C are the opposite angles, respectively.

In this case, we have:

a = AC = √2 (given) A = Angle A = 30° (given) b = BC = Рabc (what we need to find) B = Angle B = 120° (given) C = Angle C = 30° (calculated above)

Now, plug the values into the law of sines:

√2 / sin(30°) = Рabc / sin(120°)

To calculate sin(30°) and sin(120°), we need to use their trigonometric values:

sin(30°) = 0.5 sin(120°) = √3 / 2

Now, rearrange the equation and solve for Рabc:

√2 / 0.5 = Рabc / (√3 / 2)

Simplify:

√2 * 2 / 0.5 = Рabc / √3

Now, calculate the value of Рabc:

Рabc = (√2 * 2 * √3) / 0.5 Рabc = (2√6) / 0.5 Рabc = 4√6

So, the measure of side BC (Рabc) is 4√6 units.