IN RECTANGLE ABCD ,AB=25CM, BC=15CM. IN WHAT RATIO DOES BISECTOR OF ANGLE C DIVIDES AB?
To find the ratio in which the bisector of angle C divides side AB, we can use the angle bisector theorem.
The angle bisector theorem states that in a triangle, if a line bisects an angle, it divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.
In this case, the angle bisector of angle C divides side AB. Let's denote the point where the bisector intersects AB as P.
To determine the ratio in which the bisector divides AB, we need to find the lengths of AP and PB.
To do that, we need to use the information given in the problem. It states that AB = 25 cm and BC = 15 cm.
First, we need to find the length of AC using the Pythagorean theorem since we have a right triangle ABC.
Using the Pythagorean theorem, we have:
AC^2 = AB^2 - BC^2
AC^2 = 25^2 - 15^2
AC^2 = 625 - 225
AC^2 = 400
AC = √400
AC = 20 cm
Now, we have the lengths of AC, AB, and BC.
To find the ratio, we will use the angle bisector theorem.
According to the angle bisector theorem:
AP / BP = AC / BC
Substituting the values we know:
AP / BP = 20 cm / 15 cm
AP / BP = 4/3
Therefore, the bisector of angle C divides AB in a ratio of 4:3.
Of course the bisector of angle C is 45°
let the bisector hit AB at P
in triangle BCP
tan 45 = BP/15
BP = 15tan45 = 15
continue