Question

Кут між діагоналями прямокутника дорівнює 60 градусів , довжина діагоналі 10 см. Знайдіть довжину більшої сторони прямокутника

Answer 1

По теореме косинусов можно найти)
v(5^2+5^2-2*5*5*cos120)=v(25+25-50*(-1/2))=v(50+25)=v75=5v3 см

Answer 2

Finding the Length of the Longer Side of a Rectangle

To find the length of the longer side of a rectangle, given that the angle between the diagonals is 60 degrees and the length of one diagonal is 10 cm, we can use trigonometric relationships.

Let's denote the length of the longer side of the rectangle as L.

To solve this problem, we can use the fact that the diagonals of a rectangle bisect each other and form four congruent right triangles. The angle between the diagonals is 60 degrees, which means each of these right triangles has a 30-degree angle.

Using trigonometric relationships, we can determine the length of the longer side of the rectangle.

Solution:

1. Let's consider one of the right triangles formed by the diagonals of the rectangle. 2. In this triangle, the angle opposite the longer side of the rectangle is 30 degrees. 3. The length of one diagonal is given as 10 cm. 4. We can use the trigonometric relationship sin(30 degrees) = (opposite side) / (hypotenuse) to find the length of the longer side of the rectangle.

Using the trigonometric relationship, we have:

sin(30 degrees) = (L/2) / 10

Simplifying the equation, we get:

L/2 = 10 * sin(30 degrees)

To find the value of sin(30 degrees), we can refer to trigonometric tables or calculators. The value of sin(30 degrees) is 0.5.

Substituting this value into the equation, we have:

L/2 = 10 * 0.5

Simplifying further, we get:

L/2 = 5

Multiplying both sides of the equation by 2, we find:

L = 10

Therefore, the length of the longer side of the rectangle is 10 cm.

Conclusion:

The length of the longer side of the rectangle is 10 cm.