Question

Допоможіть будь ласка ... У прямокутному трикутнику ABC кут C-прямий , CD висота , BD/CD=1.3. Визначте : AD/CD. Якщо можна то повністю з розв'язанням

Answer 1

BD/CD=1/3 (дано)

∠СAD =90°-∠ACD =∠BCD

△CAD~△BCD (по двум углам)

AD/CD =CD/BD =3/1

Answer 2

Problem Analysis

We are given a right triangle ABC with angle C being a right angle. CD is the altitude of the triangle, and we are told that the ratio BD/CD is 1.3. We need to find the ratio AD/CD.

Solution

To solve this problem, we can use the properties of similar triangles. Let's consider triangle BCD and triangle ACD. Since angle C is common to both triangles, we only need to compare the ratios of the corresponding sides.

According to the given information, BD/CD = 1.3. Let's assign a value to CD to make the calculations easier. We can assume CD = 1. This means that BD = 1.3.

Now, let's consider triangle ACD. We want to find the ratio AD/CD. Since we assumed CD = 1, we need to find the value of AD.

Using the Pythagorean theorem, we can find the length of AC. In a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC). Since angle C is a right angle, we have:

AC^2 = AB^2 + BC^2

Let's assume AB = x. Then BC = 1.3x (since BD/CD = 1.3). Substituting these values into the Pythagorean theorem equation, we get:

AC^2 = x^2 + (1.3x)^2 AC^2 = x^2 + 1.69x^2 AC^2 = 2.69x^2

Taking the square root of both sides, we get:

AC = sqrt(2.69)x

Now, let's consider triangle ACD. We want to find the ratio AD/CD. Since we assumed CD = 1, we need to find the value of AD. Using the properties of similar triangles, we know that the ratio of corresponding sides in similar triangles is equal. Therefore, we have:

AD/AC = CD/BC

Substituting the values we found, we get:

AD/(sqrt(2.69)x) = 1/1.3x

Cross-multiplying, we get:

AD = (sqrt(2.69)x)/(1.3x) AD = sqrt(2.69)/1.3

Simplifying the expression, we get:

AD/CD = sqrt(2.69)/1.3

Therefore, the ratio AD/CD is equal to sqrt(2.69)/1.3.

Answer

The ratio AD/CD is equal to sqrt(2.69)/1.3.