Question

В треугольнике АБС АС=ВС=48,высота АН=24.Найдите угол С. Ответ дайте в градусах.

Answer 1

Угол будет=120 градусов.
можно найти через косинус угла С в треуг. АСН и умножить на 2

Answer 2

Given Information:

We are given the following information about triangle ABC: - AC = BC = 48 - Height AN = 24

Finding Angle C:

To find angle C, we can use the properties of right-angled triangles. Since AN is the height of triangle ABC, it is perpendicular to the base BC. Therefore, triangle ANC is a right-angled triangle.

We can use the trigonometric function tangent to find angle C. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.

In triangle ANC, the opposite side is AN and the adjacent side is NC. Therefore, we can write:

tan(C) = AN / NC

We know that AN = 24. To find NC, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In triangle ANC, the hypotenuse is AC and the other two sides are AN and NC. Therefore, we can write:

AC^2 = AN^2 + NC^2

Substituting the given values, we have:

48^2 = 24^2 + NC^2

Simplifying the equation, we get:

NC^2 = 48^2 - 24^2

Taking the square root of both sides, we have:

NC = √(48^2 - 24^2)

Now we can substitute the values of AN and NC into the equation for tangent:

tan(C) = 24 / √(48^2 - 24^2)

To find angle C, we can take the inverse tangent (arctan) of both sides:

C = arctan(24 / √(48^2 - 24^2))

Calculating the value of C using a calculator, we find that angle C is approximately 56 degrees.

Answer:

The measure of angle C in triangle ABC is approximately 56 degrees.