Question

В треугольнике авс угол с 90 ,ав =12 ,tg a=5/корень из 20 . Найти ас ?

Answer 1

Решение приложено в картинке.

Answer 2

Task: Find the value of AC in a triangle ABC with angle ACB = 90°, AB = 12, and tg(AC) = 5/√20.

To find the value of AC in the given triangle ABC, we can use the trigonometric function tangent (tg). The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Given: - Angle ACB = 90° - AB = 12 - tg(AC) = 5/√20

Let's solve this step by step:

Step 1: Identify the sides and angles in the triangle. In triangle ABC, we have: - Angle ACB = 90° (right angle) - Side AB = 12 - Side AC (unknown) - Side BC (unknown)

Step 2: Use the given information to find the value of AC. We are given that tg(AC) = 5/√20. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, AC is the opposite side, and BC is the adjacent side.

Using the tangent formula, we can write: tg(AC) = AC/BC

Substituting the given values, we have: 5/√20 = AC/BC

Step 3: Simplify the equation. To simplify the equation, we can square both sides to eliminate the square root: (5/√20)^2 = (AC/BC)^2

Simplifying further: 25/20 = (AC/BC)^2 5/4 = (AC/BC)^2

Step 4: Solve for AC. To solve for AC, we need to find the square root of both sides: √(5/4) = AC/BC

Simplifying further: √5/√4 = AC/BC √5/2 = AC/BC

Step 5: Substitute the known values. We know that angle ACB is a right angle, so we can use the Pythagorean theorem to relate the sides of the triangle: AC^2 + BC^2 = AB^2

Substituting the known values, we have: AC^2 + BC^2 = 12^2 AC^2 + BC^2 = 144

Since ACB is a right angle, we can substitute BC with AC in the equation: AC^2 + AC^2 = 144 2AC^2 = 144 AC^2 = 72

Taking the square root of both sides, we get: AC = √72

Step 6: Simplify the value of AC. To simplify the value of AC, we can factor out the perfect square: AC = √(36 * 2) AC = √36 * √2 AC = 6√2

Therefore, the value of AC in the given triangle ABC is 6√2.

Please let me know if I can help you with anything else.