Question

В прямоугольном треугольнике авс с прямым углом с проведена высота СН найдите НВ если АН=3,2 а СН=2,4

Answer 1

Высота  прямоугольного треугольника к гипотенузе является средним пропорциональным для отрезков гипотенузы.
СН²=АН*ВН
ВН= 2,4²/3,2 = 5,76/3,2=1,8.

Answer 2

Task: Finding the length of NV in a right-angled triangle

To find the length of NV in a right-angled triangle ABC, where AV is the hypotenuse and CN is the altitude, we need to use the given information that AN = 3.2 and CN = 2.4.

Let's break down the problem step by step:

1. Identify the right-angled triangle: Triangle ABC is a right-angled triangle with a right angle at vertex A.

2. Determine the relationship between the sides: In a right-angled triangle, the altitude drawn from the right angle to the hypotenuse divides the triangle into two smaller triangles that are similar to the original triangle. This means that the ratios of corresponding sides in the triangles are equal.

3. Use the similarity of triangles to find the length of NV: Since triangle ABC is similar to triangle ANC, we can set up the following proportion:

AN / AC = CN / NV

Substituting the given values, we have:

3.2 / AV = 2.4 / NV

We need to find the length of NV.

4. Solve the proportion for NV: To find the length of NV, we can cross-multiply and solve for NV:

3.2 * NV = 2.4 * AV

Dividing both sides by 3.2, we get:

NV = (2.4 * AV) / 3.2

Now, we need to find the value of AV.

5. Find the value of AV: Unfortunately, the length of AV is not provided in the given information. Without the value of AV, we cannot determine the exact length of NV.

In conclusion, we cannot find the length of NV without knowing the length of AV. If you have any further questions or need clarification, please let me know!