Question

Ребята помогите решить задачу по геометриюи: один из углов прямоугольного треугольника равен 30 градусов а сумма гепотинузы и меньшего катета равна 36 см найдите ети стороны

Answer 1

Меньший катет лежит против угла 30° и равен половине гипотенузы.
Пусть х - меньший катет, тогда 2х - гипотенуза.
Составим уравнение:
х + 2х = 36 
3х = 36
х = 36 : 3
х = 12 см  - меньший катет

гипотенуза = 2х = 2 * 12 = 24 см

Если нужно найти и больший катет (у), то по теореме Пифагора:
$y= \sqrt{24^2-12^2}= \sqrt{576-144}= \sqrt{432}= 12 \sqrt{3}$

Answer 2

Problem Analysis

We are given that one of the angles of a right triangle is 30 degrees, and the sum of the hypotenuse and the smaller leg is 36 cm. We need to find the lengths of the sides of the triangle.

Solution

Let's assume that the smaller leg of the triangle is a and the hypotenuse is c. The other leg can be found using the Pythagorean theorem.

Using trigonometric ratios, we know that the sine of an angle is equal to the ratio of the length of the opposite side to the hypotenuse. In this case, the sine of the angle 30 degrees is equal to the ratio of the length of the smaller leg to the hypotenuse.

So, we have:

sin(30) = a / c

We also know that the sum of the hypotenuse and the smaller leg is 36 cm:

c + a = 36

Now, we can solve these two equations simultaneously to find the values of a and c.

Calculation

Let's solve the equations:

From the equation sin(30) = a / c, we can substitute the value of sin(30) as 0.5:

0.5 = a / c

Multiplying both sides by c, we get:

0.5c = a

Substituting this value of a in the equation c + a = 36, we get:

c + 0.5c = 36

Simplifying, we have:

1.5c = 36

Dividing both sides by 1.5, we get:

c = 24

Substituting this value of c in the equation 0.5c = a, we get:

0.5 * 24 = a

Simplifying, we have:

a = 12

Therefore, the lengths of the sides of the triangle are: - The smaller leg (a) = 12 cm - The hypotenuse (c) = 24 cm

Answer

The lengths of the sides of the right triangle are 12 cm for the smaller leg and 24 cm for the hypotenuse.