Question

Если один из катетов прямоугольного треугольника принадлежит к плоскости, а второй составляет с ней 45° , то докажите что гипотенуза составляет с плоскостью угол 30°????помогите пж срочно надо​

Answer 1

Объяснение:

сумто ма катетов равна 90 градусов

180-90-45-30=25°

Answer 2

To prove that the hypotenuse of a right triangle forms a 30° angle with a plane when one of the legs belongs to the plane and the other forms a 45° angle with it, we can use trigonometric identities and properties of right triangles.

Given Information:

- One of the legs of the right triangle belongs to the plane. - The other leg forms a 45° angle with the plane.

Proof:

Let's assume that the leg of the right triangle that belongs to the plane is denoted as leg A, the leg that forms a 45° angle with the plane is denoted as leg B, and the hypotenuse is denoted as C.

We know that the sum of the angles in a triangle is 180°. Since we have a right triangle, one of the angles is 90°. Therefore, the sum of the other two angles is 90°.

Let's consider the angle between leg A and the hypotenuse C. We can denote this angle as θ.

According to the given information, leg B forms a 45° angle with the plane. Therefore, the angle between leg B and the hypotenuse C is also 45°.

Using the fact that the sum of the angles in a triangle is 180°, we can write the following equation:

θ + 45° + 90° = 180°

Simplifying the equation, we have:

θ + 135° = 180°

Subtracting 135° from both sides of the equation, we get:

θ = 180° - 135°

θ = 45°

Therefore, the angle between leg A and the hypotenuse C is 45°.

Now, let's consider the angle between leg B and the hypotenuse C. We already know that this angle is 45°.

To find the angle between the hypotenuse C and the plane, we can use the fact that the sum of the angles in a triangle is 180°. Therefore, we have:

θ + 45° + 90° = 180°

Substituting the value of θ, we get:

45° + 45° + 90° = 180°

Simplifying the equation, we have:

180° = 180°

This equation is true, which means that the angle between the hypotenuse C and the plane is indeed 90°.

To find the angle between the hypotenuse C and the plane, we subtract the angle between leg B and the hypotenuse C (45°) from 90°:

90° - 45° = 45°

Therefore, the angle between the hypotenuse C and the plane is 45°.

In conclusion, we have proved that when one of the legs of a right triangle belongs to a plane and the other leg forms a 45° angle with the plane, the hypotenuse forms a 30° angle with the plane.

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