Question

Два внешних угла треугольника при разных вершинах равны. Периметр треугольника равен 74 см, а одна из сторон равна 16 см. Найдите две другие стороны треугольника

Answer 1

74-16=58см(сумма двух равных сторон)58/2=29см(одна из 2х сторон)Если при двух разных вершинах треугольника 2 внешних угла равны, то равны и 2 внутренних угла этого треугольника, то есть данный треугольник - равнобедренный.Значит, две строны этого треугольника также равны. Так как в треугольнике сумма длин двух сторон всегда больше длины третьей стороны, то известная сторона может быть только основанием, а боковые стороныравны по(74-16):2=29 (см)Ответ: две другие стороны этого треугольника равны по 29 сантиметров

Answer 2

Given information:

- Two external angles of a triangle are equal. - Perimeter of the triangle is 74 cm. - One side of the triangle is 16 cm.

Let's solve this problem step by step.

Step 1: Find the measure of the equal external angles.

In any triangle, the sum of the measures of the three external angles is always 360 degrees. Since two of the external angles are equal, we can divide 360 degrees by 3 to find the measure of each external angle.

360 degrees / 3 = 120 degrees

So, each of the equal external angles measures 120 degrees.

Step 2: Find the measures of the internal angles.

The sum of the measures of the internal angles of any triangle is always 180 degrees. Since the two equal external angles are supplementary to the two internal angles at their respective vertices, we can subtract the measure of each equal external angle from 180 degrees to find the measure of each internal angle.

180 degrees - 120 degrees = 60 degrees

So, each of the internal angles measures 60 degrees.

Step 3: Find the measures of the remaining side lengths.

Since we have the measure of one side (16 cm), we can use the law of cosines to find the lengths of the other two sides.

The law of cosines states that in any triangle:

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

Where c is the side opposite to angle C, and a and b are the lengths of the other two sides.

Let's assume the side opposite to the 16 cm side is c, and the lengths of the other two sides are a and b.

We know that the measure of angle C is 60 degrees. Plugging in the values into the law of cosines, we can solve for the lengths of the other two sides.

c^2 = 16^2 + a^2 - 2 * 16 * a * cos(60)

Simplifying the equation:

c^2 = 256 + a^2 - 32a * cos(60)

Since cos(60) = 1/2, we can simplify further:

c^2 = 256 + a^2 - 16a

Similarly, we can write the equation for the other side length:

b^2 = 256 + a^2 - 16a

Step 4: Solve the equations to find the lengths of the other two sides.

We have two equations:

c^2 = 256 + a^2 - 16a b^2 = 256 + a^2 - 16a

Since c and b are equal (as given in the problem statement), we can equate the two equations:

256 + a^2 - 16a = 256 + a^2 - 16a

Simplifying the equation:

0 = 0

This equation indicates that the lengths of the other two sides can have any value as long as they are equal. Therefore, we cannot determine the exact lengths of the other two sides with the given information.

However, we can say that both of the other two sides will have the same length, and that length can be any value.

So, the two other side lengths of the triangle can be represented as "x cm" and "x cm", where x can be any real number.

Note: If there are additional constraints or information provided in the problem, we can further determine the lengths of the other two sides. But based on the given information, we cannot determine their exact values.