Question

З точки до прямої проведено дві похилі, проекції яких на пряму дорівнюють 9 см і 16 см. Знайдіть відстань від точки до прямої, якщо одна щ похилих на 5 си більша за другу

Answer 1

Все просто, теорема пифагора)

Answer 2

Finding the Distance from a Point to a Line

To find the distance from a point to a line, we can use the concept of perpendicular distance. In this case, we have two oblique lines with projections on a straight line measuring 9 cm and 16 cm. We need to find the distance from the point to the line, given that one of the oblique lines is 5 cm longer than the other.

Let's denote the shorter oblique line as x cm and the longer oblique line as x + 5 cm. We can use the concept of similar triangles to solve this problem.

Solution:

1. We can set up a proportion between the lengths of the oblique lines and their projections on the straight line. The proportion is as follows:

(x + 5) / 16 = x / 9

2. Cross-multiplying the equation, we get:

16x = 9(x + 5)

3. Expanding and simplifying the equation, we have:

16x = 9x + 45

4. Subtracting 9x from both sides, we get:

7x = 45

5. Dividing both sides by 7, we find:

x = 45 / 7

6. Simplifying the fraction, we have:

x ≈ 6.43 cm

7. Now that we have the value of x, we can find the length of the longer oblique line:

x + 5 ≈ 6.43 + 5 ≈ 11.43 cm

8. Finally, to find the distance from the point to the line, we can use the Pythagorean theorem. The distance is the hypotenuse of a right triangle formed by the shorter oblique line, the longer oblique line, and the distance from the point to the projection on the straight line.

Using the Pythagorean theorem, we have:

distance = √(x^2 + (x + 5)^2)

Substituting the values we found earlier:

distance = √(6.43^2 + 11.43^2)

Calculating this, we find:

distance ≈ 13.15 cm

Conclusion:

The distance from the point to the line is approximately 13.15 cm.