Question

Стороны параллелограмма 13 и 4 см а угол между ними 60 градусов найти меньшую диагональ ​

Answer 1

Ответ:

√133

Пошаговое объяснение:

Пусть меньшая диагональ параллелограмма d (но она же и сторона треугольника). Тогда по теореме косинусов

d^2=13^2+4^2-2*13*4*cos 60°=169+16-104*1/2=185-52=133

d=√133

Answer 2

Parallelogram and its sides

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. In this case, the given sides of the parallelogram are 13 cm and 4 cm, and the angle between them is 60 degrees.

Finding the smaller diagonal

To find the length of the smaller diagonal of the parallelogram, 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 our case, we can consider the sides of the parallelogram as the two sides of a triangle, and the angle between them as the angle opposite the diagonal. Let's denote the sides of the parallelogram as a = 13 cm and b = 4 cm, and the angle between them as C = 60 degrees.

Using the law of cosines, we can calculate the length of the smaller diagonal (c):

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

c^2 = 13^2 + 4^2 - 2 * 13 * 4 * cos(60)

c^2 = 169 + 16 - 104 * cos(60)

c^2 = 185 - 104 * 0.5

c^2 = 185 - 52

c^2 = 133

Taking the square root of both sides, we find:

c = √133

Therefore, the length of the smaller diagonal of the parallelogram is approximately √133 cm.