The side of the isosceles triangle is 5 cm and the base is 6. Find the bisector of the angle that lies opposite the base.

In an isosceles triangle, the bisector, median, and height drawn to the base are the same line.

As the height, this line divides the original isosceles triangle into two right-angled triangles, and as the median divides the base into two equal parts:

6: 2 = 3 cm

In the new triangle (let us designate its sides as a, b – legs, c – hypotenuse) a = 3, b =? (bisector), c = 5cm (by condition).

By the Pythagorean theorem:

a ^ 2 + b ^ 2 = c ^ 2;
b ^ 2 = c ^ 2 – a ^ 2;
c ^ 2 = 25 – 9;
in ^ 2 = 16;
h = 4 cm.