Question

Пожалуйста решите,не с интернета и с чертежом,ПОЖАЛУЙСТА. Прямоугольный треугольник вписан в окружность радиусом 6,5 см. найти: площадь если один из катетов = 5 см?

Answer 1

Гипотенуза вписанного треугольника является диаметром окружности. Если радиус окружности=6.5см, то гипотенуза треугольника равна  6.5·2=13см.
Найдём второй катет по теореме Пифагора : а=√(13²-5²)=√(169-25)=√144=12
SΔ=1\2·12·5=30(см²)

Answer 2

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Answer 3

Problem Analysis

We are given a right triangle inscribed in a circle with a radius of 6.5 cm. One of the legs of the triangle has a length of 5 cm. We need to find the area of the triangle.

Solution

To find the area of the triangle, we can use the formula: Area = (base * height) / 2.

In this case, the base of the triangle is one of the legs, which has a length of 5 cm. We need to find the height of the triangle.

Since the triangle is inscribed in a circle, the hypotenuse of the triangle is the diameter of the circle, which is twice the radius. Therefore, the hypotenuse is 2 * 6.5 cm = 13 cm.

Using the Pythagorean theorem, we can find the height of the triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the height of the triangle as 'h'. We have the following equation:

5^2 + h^2 = 13^2

Simplifying the equation, we get:

25 + h^2 = 169

Subtracting 25 from both sides, we get:

h^2 = 144

Taking the square root of both sides, we get:

h = 12

Now that we have the base and height of the triangle, we can calculate the area using the formula:

Area = (base * height) / 2 = (5 * 12) / 2 = 30 cm^2

Therefore, the area of the triangle is 30 cm^2.

Answer

The area of the triangle is 30 cm^2.