Question

катеты прямоугольного треугольника равны корень из 15 и 3 корня из 3.найти площадь описаного круга

Answer 1

a=sqrt(15)

b=3*sqrt(3)

R=(1/2)*sqrt(a^2+b^2)

R=(1/2)*sqrt(15+27)=(1/2)*sqrt(42)

S=pi*R^2

S=10,5*pi

Answer 2

Finding the Lengths of the Legs of the Right Triangle

To find the lengths of the legs of the right triangle, we are given that one leg is equal to the square root of 15, and the other leg is equal to 3 times the square root of 3.

Let's denote the lengths of the legs as a and b. According to the given information, we have:

a = √15 b = 3√3

Finding the Area of the Circumscribed Circle

To find the area of the circumscribed circle, we can use the fact that the diameter of the circle is equal to the hypotenuse of the right triangle.

Let's denote the diameter of the circle as d. The diameter is equal to the sum of the lengths of the legs of the right triangle:

d = a + b

To find the radius of the circle (r), we divide the diameter by 2:

r = d / 2

The area of the circle can be calculated using the formula:

Area = πr^2

Now, let's substitute the values of a and b into the equations to find the area of the circumscribed circle.

Calculation

Given: a = √15 b = 3√3

We can calculate the values of a and b:

a = √15 ≈ 3.87 b = 3√3 ≈ 5.20

Next, we calculate the diameter d:

d = a + b ≈ 3.87 + 5.20 ≈ 9.07

Then, we find the radius r:

r = d / 2 ≈ 9.07 / 2 ≈ 4.54

Finally, we calculate the area of the circumscribed circle:

Area = πr^2 ≈ π * (4.54)^2 ≈ 64.47 square units

Therefore, the approximate area of the circumscribed circle is 64.47 square units.

Please note that the calculations provided are approximations and may not be exact due to rounding.

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