Question

Срочно 40 баллов!!!!! Основание прямой призмы равнобедренный треугольник. Основание треугольника равно 6 и синус прилежащего к углу основания равен 0,6. Найдите объем призмы,если сумма площадей оснвоаний равно площади ее боковой повехности

Answer 1

Основание прямой призмы равнобедренный треугольник ABC, AB=BC; AC=6.
sinA=0.6.
cosA=sqrt(1-0.6²)=0.8;
AB=BC=(AC/2)/cosA=3/0.8=3.75;
SΔABC=AB*AC*sinA/2=3.75*6*0.6/2=3.75*1.8=6.75;
2*SΔABC=13.5;

площадь боковой повехности:
S=h*(AB+BC+AC);  h=2*SΔABC/(AB+BC+AC)=13.5/(6+3.75+3.75)=1;
объем призмы:
V=h*SΔABC=6.75;

V=6.75 !!!

Answer 2

Finding the Volume of a Prism with an Isosceles Triangle Base

To find the volume of a prism with an isosceles triangle base, we need to know the length of the base and the height of the prism. In this case, the base of the prism is an isosceles triangle with a base length of 6 units, and the sine of the angle adjacent to the base is 0.6.

To find the height of the prism, we can use the sine formula for a right triangle:

sin(angle) = opposite / hypotenuse

In this case, the opposite side is the height of the prism, and the hypotenuse is the length of the base. Let's solve for the height:

sin(angle) = height / base

0.6 = height / 6

height = 0.6 * 6

height = 3.6 units

Now that we have the height of the prism, we can calculate its volume. The volume of a prism is given by the formula:

Volume = base area * height

The base area of the prism is the area of the isosceles triangle, which can be calculated using the formula:

Base area = (1/4) * base^2 * sqrt(4 * height^2 - base^2)

Substituting the given values:

Base area = (1/4) * 6^2 * sqrt(4 * 3.6^2 - 6^2)

Calculating the base area:

Base area ≈ 9.4868 square units

Finally, we can calculate the volume of the prism:

Volume = base area * height

Volume ≈ 9.4868 * 3.6

Volume ≈ 34.151 square units

Therefore, the volume of the prism is approximately 34.151 cubic units.

Please note that the calculations provided are based on the given information and assumptions. If there are any additional details or constraints, please let me know, and I'll be happy to assist you further.