Question

Похила АМ дорівнює 10 см і утворює з площиною а кут 60° (мал. 10.3). Знайдіть проекцію похилої.​

Answer 1

Ответ:     5 см .

Объяснение:

   Похила  МА , МА = 10 см ;  МВ⊥α , ∠МАВ = 60° ;  АВ  -  ?

ΔМАВ - прямокутний ; ∠В = 90° ;  cosA = AB/MA ;  AB = MAcosA =

 = 10 * cos60° = 10 * 1/2 = 5 ( см ) ;   АВ = 5 см .

Answer 2

Похила АМ дорівнює 10 см і утворює з площиною а кут 60° (мал. 10.3). Знайдіть проекцію похилої.

Understanding the Problem

To find the projection of the inclined plane, we need to understand the given information. We are given that the inclined plane AM has a length of 10 cm and forms a 60° angle with the plane a. We need to determine the projection of the inclined plane.

Solution

To find the projection of the inclined plane, we can use trigonometry. Let's denote the projection as P.

We can use the sine function to find the length of the projection. The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse. In this case, the opposite side is the projection P and the hypotenuse is the inclined plane AM.

Using the sine function, we have:

sin(60°) = P / 10 cm

To find the value of sin(60°), we can refer to a trigonometric table or use a calculator. The value of sin(60°) is √3/2.

Substituting this value into the equation, we have:

√3/2 = P / 10 cm

To find the value of P, we can rearrange the equation:

P = (√3/2) * 10 cm

Simplifying the expression, we have:

P = 5√3 cm

Therefore, the projection of the inclined plane is 5√3 cm.

Conclusion

The projection of the inclined plane AM, which has a length of 10 cm and forms a 60° angle with the plane a, is 5√3 cm.