Question

Треугольник АВС -прямоугольный , угол В -60* ,АС-8 см , ВС-12 см найти Периметр треугольника АВС (с теоремой пожалуйста)

Answer 1

180-60-90=30 -Угол С
АВ=6 т.к. катет лежащий против угла в 30 градусов равен половине гипотинузы . А 12:2=6см
Периметр = 12+6+8=26см

Answer 2

Perimeter of a Right Triangle

To find the perimeter of a right triangle ABC, where angle B is 60 degrees, AC is 8 cm, and BC is 12 cm, we can use the Pythagorean theorem and the properties of right triangles.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have a right triangle ABC, where angle B is 60 degrees. Let's label the sides as follows: - AB is the side opposite angle A - BC is the side opposite angle B (the hypotenuse) - AC is the side opposite angle C

Using the Pythagorean theorem, we can write the equation:

AB^2 + AC^2 = BC^2 Since angle B is 60 degrees, we know that angle A is 90 degrees (because the sum of the angles in a triangle is 180 degrees) and angle C is 30 degrees (because the angles in a triangle add up to 180 degrees).

Now, let's substitute the given values into the equation:

AB^2 + 8^2 = 12^2

Simplifying the equation:

AB^2 + 64 = 144

Subtracting 64 from both sides:

AB^2 = 80

Taking the square root of both sides:

AB = √80

Simplifying the square root:

AB = 4√5

Now that we know the lengths of all three sides of the triangle, we can calculate the perimeter by adding the lengths of the three sides:

Perimeter = AB + BC + AC

Substituting the values:

Perimeter = 4√5 + 12 + 8

Simplifying the expression:

Perimeter = 4√5 + 20

Therefore, the perimeter of triangle ABC is 4√5 + 20 cm.