Question

знайти периметр прямокутного трикутника якщо один із його катетів дорівнює 6 см, а прилеглий до нього кут 30 градусів

Answer 1

Гипотенуза=6/cos30=4корня из 3 2) по теореме Пифагора: (4корня из 3)^2-36=12, извлечь корень, катет равен 2 корня из 3. 3) S=1/2*6*2корня из 3=6корней из 3!)

Answer 2

Finding the Perimeter of a Right Triangle

To find the perimeter of a right triangle, we need to know the lengths of its three sides. In this case, we are given that one of the legs (also known as a cathetus) of the right triangle is 6 cm, and the angle adjacent to it measures 30 degrees.

To find the lengths of the other two sides, we can use trigonometric ratios. In a right triangle, the sine, cosine, and tangent ratios can be used to relate the angles and side lengths.

Let's denote the given leg as side A, the hypotenuse as side C, and the other leg as side B.

Finding the Length of Side B

Since we know the length of side A and the measure of the adjacent angle, we can use the trigonometric ratio cosine to find the length of side B.

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. In this case, the adjacent side is side A and the hypotenuse is side C.

Using the cosine ratio, we have:

cos(30 degrees) = A / C

Substituting the given values, we get:

cos(30 degrees) = 6 cm / C

To solve for C, we can rearrange the equation:

C = 6 cm / cos(30 degrees)

Now, we can calculate the value of C using the cosine function.