Question

Помогите!!!Точка находится от прямой на расстоянии 5 см. От неё к прямой проведено наклонную , которая образует с прямой угол 45град. Найдите проекцию наклонной на эту прямую!

Answer 1

Расстрояние от точки до прямой - это длина перпендикуляра от точки до прямой.
Длина перпендикуляра : проекцию наклонной= tg45
5: проекцию=1
проекция=5

Answer 2

Problem Analysis

We are given a point that is 5 cm away from a straight line. A slant line is drawn from the point to the straight line, forming a 45-degree angle with the straight line. We need to find the projection of the slant line onto the straight line.

Solution

To find the projection of the slant line onto the straight line, we can use trigonometry. Let's assume the point is A, the straight line is BC, and the slant line is AD.

1. Draw a perpendicular line from point A to the straight line BC. Let's call the point of intersection E. 2. Now we have a right triangle ABE, where AB is the distance between the point A and the straight line BC, and AE is the projection of the slant line AD onto the straight line BC. 3. We know that AB = 5 cm (given in the problem statement) and the angle BAE is 45 degrees (also given in the problem statement). 4. To find AE, we can use the trigonometric function cosine. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, AE is the adjacent side and AB is the hypotenuse. - AE = AB * cos(BAE)

Let's calculate the value of AE using the given information.

Calculation

AE = AB * cos(BAE)

Given: AB = 5 cm BAE = 45 degrees

Using the formula: AE = 5 cm * cos(45 degrees)

Calculating the value: AE = 5 cm * 0.7071 AE ≈ 3.54 cm

Answer

The projection of the slant line onto the straight line is approximately 3.54 cm.