Question

3. Знайдіть радіус кола, описаного навколо рівнобедреного трикутника, якщо його основа та висота вiдповiдно дорівнюють:20 см i 26 см.​

Answer 1

Ответ:24см

Объяснение:

У рівнобедр. трикут. висота проведена до його основи є одночасно і медіаною, і бісектрисою.

З одного прямокут. трикут. знайдемо катет.

За теоремою Піфагора с=√(a^2+b^2)(a

2

+b

2

) , з цієї формули знайдемо а

a= √(c^2-b^2)(c

2

−b

2

) , тоді

а= √(26^2-10^2)(26

2

−10

2

) =√(676-100)=√576= 24

Відповідь: 24 см

Answer 2

Finding the Radius of the Circumscribed Circle

To find the radius of the circle circumscribed around an isosceles triangle, we can use the formula:

Radius of the circumscribed circle = (1/2) * (base / sin(angle))

In this case, since the triangle is isosceles, the base and the height are related. We can use the Pythagorean theorem to find the length of the sides and then calculate the radius of the circumscribed circle.

Calculating the Radius

Given: - Base of the isosceles triangle = 20 cm - Height of the isosceles triangle = 26 cm

Using the Pythagorean theorem, we can find the length of the sides of the isosceles triangle. Let's denote the base and the two equal sides of the triangle as b, a, and a respectively.

The Pythagorean theorem states that: c^2 = a^2 + b^2

Where c is the hypotenuse (the side opposite the right angle) and a and b are the other two sides.

Solving for the sides of the triangle: a^2 = (26 cm)^2 - (10 cm)^2 a^2 = 676 cm^2 - 400 cm^2 a^2 = 276 cm^2 a = √276 cm a ≈ 16.6 cm

Now that we have the length of the sides, we can calculate the radius of the circumscribed circle using the formula mentioned earlier.

Calculating the Radius of the Circumscribed Circle

Using the formula: Radius of the circumscribed circle = (1/2) * (base / sin(angle))

In an isosceles triangle, the angle opposite the base is the apex angle. We can find the apex angle using the sine function: sin(angle) = opposite / hypotenuse sin(angle) = 10 cm / 16.6 cm sin(angle) ≈ 0.6024 angle ≈ sin^(-1)(0.6024) angle ≈ 37.1 degrees

Now, we can calculate the radius: Radius of the circumscribed circle = (1/2) * (20 cm / sin(37.1 degrees)) Radius ≈ (1/2) * (20 cm / 0.6024) Radius ≈ 16.6 cm

So, the radius of the circle circumscribed around the isosceles triangle with a base of 20 cm and a height of 26 cm is approximately 16.6 cm.