Question

один з катетів прямокутного трикутника дорівнює 30 см а радіус описаного навколо нього кола 17 см обчисліть площу даного трикутника​

Answer 1

Ответ:  240 см².  

Объяснение:

Центр описанного круга вокруг прямоугольного треугольника находимся на гипотенузе и делит его пополам.

R=17 см

AC=30 см

AB=2R=34 см

---------

S=1/2AC*BC.

По т. Пифагора

BC=√(AB²-AC²)=√(34²-30²)=√(1156-900) = √256=16 см.

S=1/2*30*16 = 15*16 = 240 см².  

(См. скриншот).

Answer 2

Calculation of the Area of a Right Triangle

To calculate the area of a right triangle, we need to know the lengths of its two perpendicular sides, also known as the legs. In this case, one of the legs of the right triangle is given as 30 cm.

Let's denote the length of the other leg as 'x'. According to the given information, the radius of the circle circumscribed around the triangle is 17 cm. The radius of the circumscribed circle is equal to half the length of the hypotenuse of the right triangle.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

c^2 = a^2 + b^2

where 'c' is the length of the hypotenuse, and 'a' and 'b' are the lengths of the legs.

In this case, we have:

c^2 = 30^2 + x^2

Since the radius of the circumscribed circle is equal to half the length of the hypotenuse, we can write:

17 = c/2

Solving these two equations simultaneously will allow us to find the value of 'x' and subsequently calculate the area of the triangle.

Let's proceed with the calculations.