Question

СРОЧНО!!! Найдите площадь боковой поверхности прямой треугольной призмы , если известно, что одна из сторон основания равна 7 см, другая- 8 см, косинус угла между ними равен 2/7 , а боковое ребро призмы равно 11 см

Answer 1

Sбок=pH=(AB+AC+BC),АВ=8см,АС=7см,соs< А=2/7.Тогда по т.косинусов найдем ВС:
                 ВС= √(AB^2+AC^2-AB*AC соs< А)
                BC= √64+49-2*8*7*2/7=√ 64+49-32=√81=9.
Тогда имеем: Sбок =(8+7+9)11=24*11=264 (см кв.)

            Ответ: Sбок=264 см кв. 

Answer 2

Calculation of the lateral surface area of a right triangular prism

To find the lateral surface area of a right triangular prism, we need to know the lengths of the two sides of the base, the cosine of the angle between them, and the length of the lateral edge.

Given: - One side of the base = 7 cm - Another side of the base = 8 cm - Cosine of the angle between the sides = 2/7 - Length of the lateral edge = 11 cm

To calculate the lateral surface area, we can use the formula:

Lateral Surface Area = (Perimeter of the base) x (Length of the lateral edge)

The perimeter of the base can be calculated using the lengths of the two sides of the base and the cosine of the angle between them. Let's calculate the perimeter of the base first.

The third side of the base can be found using the Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where: - c is the length of the third side of the base - a and b are the lengths of the two known sides of the base - C is the angle between the two known sides

Let's calculate the length of the third side of the base:

c^2 = 7^2 + 8^2 - 2 * 7 * 8 * (2/7)

Simplifying the equation:

c^2 = 49 + 64 - 32

c^2 = 81

Taking the square root of both sides:

c = 9

Now that we have the lengths of all three sides of the base, we can calculate the perimeter:

Perimeter of the base = 7 + 8 + 9 = 24 cm

Finally, we can calculate the lateral surface area:

Lateral Surface Area = 24 cm x 11 cm = 264 cm^2

Therefore, the lateral surface area of the given right triangular prism is 264 cm^2.

Please note that the calculations provided are based on the information given and may vary depending on the specific context or problem statement.