Question

у прямокутному трикутнику ABC кут доривнюе 60 градусов катет BC доривнюе 6 сантиметров Найдите гипотенузу AB ​

Answer 1

Ответ:

12 см

Объяснение:

кут САВ = 30° (за умовою)

сторона,ьщо лежить напроти кута 30° = половина гіпотинузи.

сторона СВ лежить напроти САВ, тому гіпотинуза АВ = 6×2=12 см

Answer 2

Відповідь:     АВ = 12 см .

Пояснення:

Нехай у прямок. ΔАВС   ∠С = 90° ;   ∠В = 60°, тоді ∠А = 90° - 60°= 30°.

За власт. катета , що лежить проти кута 30°   ВС =1/2 АВ ;  ----->

AB = 2* BC = 2 * 6 = 12 ( см ) ;    АВ = 12 см .

Answer 3

Finding the Hypotenuse of a Right Triangle

To find the length of the hypotenuse (AB) of a right triangle ABC, we can use the Pythagorean theorem. 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.

In this case, we are given that angle BAC is 60 degrees and the length of one of the legs, BC, is 6 centimeters. We need to find the length of the hypotenuse, AB.

Let's denote the length of AB as x. According to the Pythagorean theorem, we have the following equation:

AB^2 = BC^2 + AC^2

Since angle BAC is 60 degrees, we know that angle BCA is 90 - 60 = 30 degrees. Therefore, triangle BCA is a 30-60-90 triangle.

In a 30-60-90 triangle, the ratio of the lengths of the sides is 1 : √3 : 2. This means that the length of AC is BC * √3.

Substituting the values into the equation, we have:

x^2 = 6^2 + (6√3)^2

Simplifying the equation:

x^2 = 36 + 36 * 3

x^2 = 36 + 108

x^2 = 144

Taking the square root of both sides, we find:

x = √144

Calculating the square root of 144, we get:

x = 12

Therefore, the length of the hypotenuse AB is 12 centimeters.