Question

Стороны треугольника равны 40 дм, 60 дм и 80 дм на какие части делит биссектриса большего угла треугольника противоположную сторону

Answer 1

Биссектрисса делит противолежащую сторону пропорционально прилежащим сторонам.
Больший угол - угол, противолежащий большей стороне, а большая сторона - 80 дм
разбита она будет на части x дм b 80-х дм
х/40 = (80-х)/60
х/2 = (80-х)/3
3х = 2(80-х)
3х = 160 - 2х
5х = 160
х = 160/5
х = 32 дм - это меньший отрезок
80 - х = 80 - 32 = 48 дм - это больший отрезок

Answer 2

Bisector of the Larger Angle of a Triangle Dividing the Opposite Side

When the sides of a triangle are 40 dm, 60 dm, and 80 dm, the bisector of the larger angle of the triangle divides the opposite side in the following way:

The bisector of the larger angle of a triangle divides the opposite side into segments that are proportional to the other two sides of the triangle. This is known as the Angle Bisector Theorem.

In this case, the larger angle of the triangle is opposite the side measuring 80 dm. Let's denote the points where the bisector intersects the opposite side as P and Q. According to the Angle Bisector Theorem, the ratio of the segments of the opposite side created by the bisector is equal to the ratio of the other two sides of the triangle that form the larger angle.

Using the given side lengths: - The side lengths are 40 dm, 60 dm, and 80 dm. - The bisector of the larger angle divides the opposite side into segments in a specific ratio.

Applying the Angle Bisector Theorem: - The ratio of the segments of the opposite side created by the bisector is equal to the ratio of the other two sides of the triangle that form the larger angle.

Let's calculate the ratio and the lengths of the segments using the given side lengths.

Calculation: - The ratio of the segments of the opposite side created by the bisector is 60:40, which simplifies to 3:2. - Using this ratio, the lengths of the segments can be calculated.

Therefore, the bisector of the larger angle of the triangle with sides measuring 40 dm, 60 dm, and 80 dm divides the opposite side into segments in the ratio of 3:2.

This information is based on the Angle Bisector Theorem and the given side lengths of the triangle.