Question

у трикутнику зі сторонами 7 см, 15 см, 20 см проведено бісектрису меншого кута. На які відрізки бісектриса поділила меншу сторону?

Answer 1

Трикутник АВС, АВ=7, ВС=15, АС=20, в трикутнику проти меньшої сторони лежить меньший кут, СК-бісектриса, ВК=х, АК=7-х, ВК/АК=ВС/АС, х/7-х=15/20, 20х=105-15х, 35х=105, х=3=ВК, АК=7-3=4

Answer 2

Triangle with Side Lengths 7 cm, 15 cm, and 20 cm

To find out how the bisector of the smaller angle divides the smaller side of a triangle with side lengths of 7 cm, 15 cm, and 20 cm, we can use the angle bisector theorem.

The angle bisector theorem states that in a triangle, the angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

Let's denote the sides of the triangle as follows: - The side opposite the smaller angle is denoted as 'a' and has a length of 7 cm. - The side opposite the larger angle is denoted as 'b' and has a length of 15 cm. - The remaining side is denoted as 'c' and has a length of 20 cm.

We want to find out how the bisector of the smaller angle divides side 'a'.

According to the angle bisector theorem, the ratio of the lengths of the segments formed by the bisector is equal to the ratio of the lengths of the other two sides.

Let's denote the lengths of the segments formed by the bisector as 'x' and 'y'. The ratio of these segments is given by:

x / y = b / c Substituting the given values, we have:

x / y = 15 / 20

Simplifying the ratio, we get:

x / y = 3 / 4

This means that the bisector of the smaller angle divides the smaller side into segments of lengths 3 cm and 4 cm.

Therefore, the bisector divides the smaller side of the triangle with side lengths 7 cm, 15 cm, and 20 cm into segments of lengths 3 cm and 4 cm.

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