Question

Из точки А ,удаленной от прямой b на расстояние 7 см,проведены к ней перпендикуляр АВ и наклонная АС( В и С принадлежат прямой b) Найдите ВС,если угол САВ= 45°.

Answer 1

Решение задания смотри на фотографии

Answer 2

Problem Analysis

We are given a point A that is located at a distance of 7 cm from a line b. From point A, a perpendicular AB is drawn to line b, and a line AC is drawn at an angle of 45 degrees with line AB. We need to find the length of line segment BC.

Solution

To find the length of line segment BC, we can use trigonometry and the given information.

Let's denote the length of line segment BC as x.

Since angle SAB = 45 degrees, we can use the trigonometric relationship between the sides of a right triangle to find the length of AB.

Using the sine function, we have:

sin(SAB) = AB / AS

Since angle SAB = 45 degrees and AS = 7 cm, we can substitute these values into the equation:

sin(45) = AB / 7

Simplifying, we find:

AB = 7 * sin(45)

Now, we can use the cosine function to find the length of BC.

Using the cosine function, we have:

cos(SAB) = BC / AB

Since angle SAB = 45 degrees and AB is the length we just calculated, we can substitute these values into the equation:

cos(45) = x / (7 * sin(45))

Simplifying, we find:

x = (7 * sin(45)) * cos(45)

Now, we can calculate the value of x using the given information.

Calculation

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

Using a calculator, we find:

sin(45) = 0.7071 cos(45) = 0.7071

Substituting these values into the equation, we have:

x = (7 * 0.7071) * 0.7071

Simplifying, we find:

x ≈ 3.5355 cm

Therefore, the length of line segment BC is approximately 3.5355 cm.

Answer

The length of line segment BC is approximately 3.5355 cm.