Question

В треугольнике АВС угол С равен 90^ СН высота АН =4 СН=3 Найдите ВС

Answer 1

Так ch высота или ah?

Answer 2

Task: Find the length of VS in triangle ABC, where angle C is 90 degrees, AN is 4, and CN is 3.

To find the length of VS in triangle ABC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given that angle C is 90 degrees, AN is 4, and CN is 3. We need to find the length of VS.

Let's denote the length of VS as x.

Using the Pythagorean theorem, we can set up the following equation:

AC^2 = AN^2 + CN^2

Substituting the given values, we have:

AC^2 = 4^2 + 3^2

Simplifying, we get:

AC^2 = 16 + 9 AC^2 = 25

Taking the square root of both sides, we find:

AC = 5

Now, we can use the fact that AC is the hypotenuse of triangle ABC to find the length of VS. Since VS is perpendicular to AC, it is also perpendicular to BC.

Therefore, triangle BVS is similar to triangle BAC, as they share angle B and angle VBS is a right angle.

Using the property of similar triangles, we can set up the following proportion:

BV/BA = VS/AC

Substituting the known values, we have:

BV/5 = x/5

Simplifying, we find:

BV = x

Therefore, the length of VS is 5.

Answer:

The length of VS in triangle ABC, where angle C is 90 degrees, AN is 4, and CN is 3, is 5.