Question

Точка H является основанием высоты BH,опущенной из вершины прямого угла B треугольника ABC к гипотенузе AC.Найдите AC,если AB=18 и AH=8. Пожалуйста,можно с объяснением и рисунком?

Answer 1

Треугольники АВН и АВС подобны, т.к. все их углы равны

т.о. соответствующие стороны пропорциональны, см рис

Answer 2

Finding the Length of AC in Triangle ABC

To find the length of AC in triangle ABC, we can use the concept of similar triangles and the Pythagorean theorem.

Given: - AB = 18 - AH = 8

We know that point H is the base of the altitude BH, which is dropped from the vertex of the right angle B to the hypotenuse AC.

To solve for AC, we can use the following steps:

Step 1: Identify the similar triangles In triangle ABC, we have two similar triangles: triangle ABH and triangle ABC. This is because angle BAH is a right angle, and angle BAC is shared by both triangles.

Step 2: Set up a proportion Since the triangles are similar, we can set up a proportion using the corresponding sides. The corresponding sides in this case are AB and AC.

AB/AC = AH/AB

Step 3: Solve the proportion Substitute the given values into the proportion and solve for AC:

18/AC = 8/18

Cross-multiply to get:

18 * 8 = AC * 18

Simplify:

144 = AC * 18

Divide both sides by 18 to isolate AC:

AC = 144/18

Simplify further:

AC = 8

Therefore, the length of AC is 8.

Explanation with Diagram

Here is a diagram to help visualize the problem:

         A
        /|
       / |
   AC /  | BH
     /   |
    /    |
   /     |
  B______H
   \     |
    \    |
     \   |
      \  |
       \ |
        \|
         C

In the diagram, triangle ABC is a right triangle with the right angle at B. Point H is the base of the altitude BH, which is dropped from the vertex of the right angle B to the hypotenuse AC.

Using the given values, we can find the length of AC by setting up a proportion between the corresponding sides of the similar triangles ABH and ABC. Solving the proportion gives us AC = 8.

I hope this explanation helps! Let me know if you have any further questions.