Question

сторона АВ параллелограмма АВСD равна 24 см,угол А=60 градусов.найти проекцию стороны АВ на прямую AD? спасибо заранее)

Answer 1

Given Information

We are given the following information: - Side AB of parallelogram ABCD is 24 cm. - Angle A is 60 degrees.

Solution

To find the projection of side AB onto line AD, we need to find the length of the perpendicular from point B to line AD.

Let's denote the projection of AB onto AD as P. We can create a right triangle APB, where AP is the perpendicular from B to AD.

Since ABCD is a parallelogram, opposite sides are equal in length. Therefore, side AD is also 24 cm.

To find the length of AP, we can use trigonometry. In right triangle APB, angle A is 60 degrees, and we know the length of side AB is 24 cm.

Using the trigonometric function cosine, we can relate the adjacent side (AP) to the hypotenuse (AB) and the angle A:

cos(A) = AP / AB

Substituting the known values:

cos(60) = AP / 24

Simplifying:

1/2 = AP / 24

Cross-multiplying:

AP = 24 * (1/2) = 12 cm

Therefore, the projection of side AB onto line AD is 12 cm.

Answer

The projection of side AB onto line AD is 12 cm.