Question

Катета прямоугольного треугольника лежит против угла в 15 градусов найдите второй катет этого треугольника не используя тригонометрические функции угла

Answer 1

Если без тригонометрии, то поможет воспоминание о том, что 
радиус описанной около прямоугольного треугольника окружности равен половине гипотенузы и медиана к гипотенузе равна радиусу описанной окружности...
т.е. угол в 15°--это вписанный угол для окружности, (а) -хорда...
интересно рассмотреть центральный угол, стягиваемый хордой (а)... 
катет против угла в 30° равен половине гипотенузы (это без тригонометрии)) или то же самое, но короче: sin(30°) = 0.5

Answer 2

Finding the Second Leg of a Right Triangle

To find the second leg of a right triangle without using trigonometric functions, we can use the properties of special right triangles, such as the 30-60-90 triangle.

In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2. The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3 times the length of the shorter leg.

Since the given angle is 15 degrees, we can construct a 30-60-90 triangle by bisecting the given angle. This will create a right triangle with a 30-degree angle, a 60-degree angle, and a 90-degree angle.

Let's assume that the length of the shorter leg (opposite the 30-degree angle) is 'x'. According to the properties of a 30-60-90 triangle, the length of the longer leg (opposite the 60-degree angle) will be √3 times 'x'.

Therefore, the second leg of the right triangle can be found by multiplying the length of the shorter leg by √3.

Second leg = x * √3

Please note that we don't have the specific length of the shorter leg or any other information to calculate the exact value of the second leg. However, the formula provided above will give you the relationship between the lengths of the legs in a 30-60-90 triangle.

I hope this helps! Let me know if you have any further questions.