In the triangle ABC, it is known that AB = BC = 25, BH. find the length of the segment AC.

In the ABC triangle it is known:

AB = BC = 25;
BM – height = 24;
Find the length of the segment AC.

Solution:

1) Since the triangle is isosceles, then the height from the top B to the base of the AC divides the AC side in half.

2) Consider a right-angled triangle ABM with a right angle M.

sin a = BM / AB;

Substitute the known values and calculate the sine of angle A.

sin a = 24/25;

Then:

AM = √ (AB ^ 2 – BM ^ 2) = √ (25 ^ 2 – 24 ^ 2) = √ ((25 – 24) * (25 + 24)) = √ (1 * 49) = √49 = √ 7 ^ 2 = 7;

3) AC = 2 * AM = 2 * 7 = 14.

As a result, we got AM = 14.