Question

Помогите срочно с рисунком нужно 1. В остроугольном треугольнике АВС серединные перпендикуляры сторон АВ и ВС пересекаются в точке О, ОВ=10 см. Найдите расстояние от точки О до стороны АС, если угол ОАС равен 30°. ​

Answer 1

Ответ:

Точка пересечения серединных перпендикуляров треугольника - это центр его описанной окружности, значит ОА=ОВ=10 см.

Поскольку расстояние от точки О до стороны АС - это перпендикуляр к стороне АС, угол ОАС=30⁰, и зная, что катет, лежащий против угла в 30⁰ равен половине гипотенузы (в нашем случае это ОА), находим искомое расстояние 10/2=5 см.

Answer 2

To find the distance from point O to side AC in an acute-angled triangle ABC, we can use the concept of the circumcenter. The circumcenter is the point of intersection of the perpendicular bisectors of the sides of a triangle.

Given that the mid-perpendiculars of sides AB and BC intersect at point O and OB = 10 cm, we can determine the distance from point O to side AC.

Let's break down the problem step by step:

Step 1: Drawing the Triangle

First, let's draw an acute-angled triangle ABC.

Step 2: Finding the Circumcenter

Next, we need to find the circumcenter of triangle ABC. The circumcenter is the point of intersection of the perpendicular bisectors of the sides.

In this case, the mid-perpendiculars of sides AB and BC intersect at point O.

Step 3: Determining the Distance

To find the distance from point O to side AC, we need to draw a line from point O perpendicular to side AC. Let's call the point of intersection X.

Now, we have a right triangle OAX, where OA is the radius of the circumcircle and AX is the distance from point O to side AC.

We are given that the angle OAS is 30°. Since OA is the radius of the circumcircle, it is equal to OB, which is 10 cm.

To find the distance AX, we can use trigonometry. In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the hypotenuse.

In this case, sin(30°) = AX / OB.

We can rearrange the equation to solve for AX:

AX = OB * sin(30°)

Substituting the given values:

AX = 10 cm * sin(30°)

Using a calculator, we can find the value of sin(30°) to be 0.5.

AX = 10 cm * 0.5

AX = 5 cm

Therefore, the distance from point O to side AC is 5 cm.

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