Question

В треугольнике авс угол с прямой сн высота найдите тангенс угла асн

Answer 1

Тангенс угла АСН=АН/СН
чисел нет поэтому в общем виде

Answer 2

Task: Find the tangent of angle A in triangle ABC, where angle A is opposite side a and the height from point C to side AB is h.

To find the tangent of angle A in triangle ABC, we can use the formula for tangent in a right-angled triangle, which is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Given: - Side a = 4 - Side b = 6 - Side c = 9 - Height h = ?

Solution:

Using the given information, we can calculate the height h using the formula for the area of a triangle:

Area of triangle ABC = (1/2) * base * height

We can solve for the height h using the area of the triangle and the length of side b.

Area of triangle ABC = (1/2) * b * h

Now, we can calculate the area of the triangle using Heron's formula:

Area of triangle ABC = sqrt(s * (s - a) * (s - b) * (s - c))

Where s is the semi-perimeter of the triangle: s = (a + b + c) / 2

Let's calculate the semi-perimeter s: s = (4 + 6 + 9) / 2 = 19 / 2 = 9.5

Now, we can calculate the area of the triangle: Area of triangle ABC = sqrt(9.5 * (9.5 - 4) * (9.5 - 6) * (9.5 - 9))

Area of triangle ABC ≈ 9.9216

Using the area of the triangle, we can solve for the height h: 9.9216 = (1/2) * 6 * h h = (2 * 9.9216) / 6 h ≈ 3.3072

Now that we have the height h, we can find the tangent of angle A using the given information:

tan(A) = Opposite / Adjacent tan(A) = h / a tan(A) ≈ 3.3072 / 4 tan(A) ≈ 0.8268

Therefore, the tangent of angle A in triangle ABC is approximately 0.8268.